Broad differencesIn Go, every point is worth the same amount at the end. It takes a few moves (say 6) to complete control an area of your choosing even if your opponent plays closer, and it takes less (say 3) to secure it (as long as you defend it correctly). So Go has lots of little subgoals of securing larger areas, and negotiating over boundaries. The basic theory is that every move mostly affects the four neighbouring positions around it, attacking or defending them. Attacks on weak points are most threatening, and allow profit at the other three positions if the opponent must respond. However, only if an attack works, does it gain anything (from that neighbour).
Like Chess, friendly pieces almost always help, and the strength of your position is close to proportional to the number of them, throughout the game. However the position is more dynamic since pieces and move, and "commitment" mostly applies only to pawn structure, or other things you can't get back, such as the colour of your bishop, or the time it takes to move a knight to the other side of the board.
This is quite different to Othello, which I have little experience in, but which seems more random. But since it is apparently PSPACE-complete, perhaps it just needs more insight to allow preparation. Only the corners can possibly be pass-alive like in Go, so almost nothing is secure. But yet, for the game to finish at the end with secure points for each side, security must move from "capturable" to "uncapturable" over the course of the game. In Go, this tends to occur locally very quickly, whereas my impression is that it only occurs at the very end in Othello. Even the strongest players can lose by large margins to each other. You are only allow to play a move when you have a "clear line of sight" to it (with only the opponents pieces in the way), so the theoretical bases are about maximising the mobility or these lines of sight.
However Chess only has one key goal which is the capture of the opponent's king before your own (the etymology of chess is related to shah which translates to king). All positions are equal except for the initial configuration and the queening squares. Fortresses akin to Go are possible where if the opponent has few enough fighting pieces, then as long as you don't deviate, you can always defend your king. Though you won't necessarily be able to attack the opponent. So draws (by repetition, stalemate) may well be the best result. A king is able to slowly run away, but there is only finite space.
However, we can think of all such games as occurring in an abstract realm of space and time. This becomes a natural way to differentiate aspects of the game. For example referring to notes on complexity of Go problems, in the simplest positions, groups are just one move away from being captured, whereas in more difficult positions, there are multiple vital points and entrance points that either side can attack from, with more space.
Flows of valueIn Go, control over secure areas is mostly fixed, and play is about balancing the development potential of each area and preemptively preventing the opponent from threatening your areas. If they have a valuable threat, you would like to have a valuable defense in return. This occurs because pieces can't move. However in practice "influence" can shift as mentioned above. If an area dominated by Black is attacked by White, they don't have to defend it as they can't turn it into territory with one move, but an attack may compensate by gaining influence on the other side of it. In top play, the accounting will balance so that the value of the gain is close to what was lost (plus or minus the time cost of playing a move). We can think of the influence as being able to move, but only if the opponent comes close. And certain weak points have very standard ways of moving with proper shape or counterattacks/defence points if the opponent attacks. Also, consider haengma. All value is local, and only masters need to consider long term global interactions.
In Chess, all pieces can move, but only in certain ways. So when defending, you only need to cope with fixed sorts of attacks, with a complex dance of manoeuvring with counterthreats. It seems there are many cascading critical points. There is a lack of time to make the situation as perfect as in Go since the situation keeps changing. If the opponent has no bishop, then you can leave diagonal weaknesses in your position for example. They may still be attacked by the queen, but the queen might be able to do less, since you are unwilling to sacrifice it to take out the opponents defence. In a way everything is position and manoeuvers with poking at the boundaries. There are subgoals of queening pawns, but early on, they are often distractions compared to king security (at least for weaker players).
Pawns are the weakest pieces, but they are at the boundary, and attacks must be made in coordination with their structure since they are so "dumb" that they can't move backwards, so they partially fix the shape from changing. Depending on the position, some pieces might be more valuable in your defence, and if they are necessary enough that they are irreplacable the opponent may suddenly (a la Tal) sacrifice one of their more valuable pieces since it allows sufficient attack on your king (perhaps enough that you will have to bring in a more valuable piece to the defence which can then be captured or else get checkmated, or simply that you lack time and resources to prevent a perpetual).
In Chess you have to make a move, and sometimes that means breaking your defence, especially if you only have pawns and vital defenders remaining. The AI has demonstrated more subtle concepts of using pushing pawns to control more space and break the opponent with zugzwang.
In Go, you have defensible positions fixed in shape, but all Chess positions are different, and thinking in terms of completing a defense is probably not for the strongest players, since chess is more dynamic with lots of tension and constant renewal of computation is required to defend as the shape changes. Perhaps it is just my inexperience, but I think that Go language and Go mathematics is more relevant to strength than anything similar in Chess. The concepts required for Chess are often tactical and hence unique to its ruleset. They can be memorised. Perhaps there is a reason that Go is played on a larger board. Still, "optimisation of positional advantages" remains interesting in any game, and maths can provide many helpful insights with proof.
BrilliancySacrifice of more valuable pieces is often what is called a brilliancy in Chess (at least for weaker material based players), since this is so surprising to both sides.
In Go, there are such things as "tesuji" which settle a position by attacking/defending the weak points, and AI games often have a flurry of them that are very complicated. They are surprising because they attack from "inside" the opponent's region (normally you profit from an attack by playing on the outside and forcing the opponent to retreat inside), but when the opponent is weak enough and you are strong enough, sometimes this allows you to capture more stones.
TemperatureIn Go, temperature is the basis of much theory, since optimal play is about accounting for fixed sources of value. Physicists shouldn't read much more than this from the concept's name. In Chess, you can give numbers to the values of pieces, and that was mostly sufficient for Deep Blue. However, as the value of pieces depends on the positions, perhaps non-equilibrium thermodynamics becomes more relevant.
BoundariesAs in any two player game that is settled by "control" over some intersection, at the end of the game, key intersections are either controlled by black or white. However, how does this get settled before the end of the game. Most often, we talk of boundaries (mostly in space), between what is most likely Black control and what is most likely White control.
In Chess we have more defence oriented structures or more attacking oriented. In Go, we have thick and thin. In Go, if we have large territories (such as in the endgame), the fighting is about what profit can be made at the boundary, and profit is largest if we can threaten to penetrate the large territories (which is only possible against thin groups). In a sense, this is like the defence of the king in chess, except that each boundary tends to be independent. In Go, thin coverings are most easily punctured or lived in by making threats to cut (and divide and conquer), and yet that tends to mean they likely weren't worth much anyway (no man's land, not territory for either side), or that the opponent has their own problems to worry about such that they don't have time to both attack and defend. Yet this requires strength to manage, and this is the sort of Go intensity and reading out tactics that top players worry about.
In both games, you fight for control of vital points and breaking through. However in Chess, both sides get lamer with the exchange of pieces, and we can say that "empty space" wins. Whereas in Go, the capturer tends to have very strong local control, so areas tend to get increasingly solidified, and one of the players wins. Perhaps there is a reason we avoid draws in Go?
Case study: Go shimariI present my updated thinking about weak points in Go. AlphaGo shocked us with new variations of attaching to shimaris. Why?
Against a single corner stone, the corner is the main weak point and moves should threaten to chip away the corner (perhaps by capturing the first player's move if you have enough support), Moves are more valuable since they have a larger threat.
Against a shimari which is only two stones in the corner, they control the corner better regardless of if the opponent approaches (6-3 was the traditional approach to the 4-3 3-6 enclosure), so threats to cut through become more valuable locally if they also cut off the main development of the shimari. This is less valuable than getting the corner, but still one of the top opening moves (say move 8-20). However, since you will have less access to the corner, you have less eyespace, and therefore you are more vulnerable to attack. Hence, control of the side (say the middle star point) becomes more important for securing the development value of shimaris. Note that control isn't strong without eyespace, so normally, neither side plays around the middle star point directly, unless they have support (normally by approaching the opponent's corner). Also, moves from the centre maintain threats against such weak points, so there is still plenty of value to fight over even if one side or the other adds a move.