On the page you linked, here was a diagram for reducing:
$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . O . . . |
$$ | . . . , . . . . 1 , . . . . . . O . . |
$$ | . . . X . . . . . X . . . . . X O . . |
$$ | . . . . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . O . . . |
$$ | . . . , . . . . 1 , . . . . . . O . . |
$$ | . . . X . . . . . X . . . . . X O . . |
$$ | . . . . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
White is not trying to live or split black on the side. Black can simply block, and he will still get territory on the bottom:
$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . O . . . |
$$ | . . . , . . . . 1 , . . . . . . O . . |
$$ | . . . X . . . . 2 X . . . . . X O . . |
$$ | . . . . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . O . . . |
$$ | . . . , . . . . 1 , . . . . . . O . . |
$$ | . . . X . . . . 2 X . . . . . X O . . |
$$ | . . . . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
But the idea is, white has
reduced black's potential to make more territory in the area. For example, if they continue simply:
$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . O . . . |
$$ | . . . , . 7 5 3 1 , . . . . . . O . . |
$$ | . . . X . . 6 4 2 X . . . . . X O . . |
$$ | . . . . . . x x x x . . . . X . X . . |
$$ | . . . . . . x x x x . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . O . . . |
$$ | . . . , . 7 5 3 1 , . . . . . . O . . |
$$ | . . . X . . 6 4 2 X . . . . . X O . . |
$$ | . . . . . . x x x x . . . . X . X . . |
$$ | . . . . . . x x x x . . . . . . . . . |
$$ ---------------------------------------[/go]
White is conceding to allow black to make points in the marked area - but not higher than that. For example, if black had played first:
$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . B . . . . . O . . . |
$$ | . . . , . x x x x , . . . . . . O . . |
$$ | . . . X . x x x x X . . . . . X O . . |
$$ | . . . . . x x x x . . . . . X . X . . |
$$ | . . . . . x x x x . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . B . . . . . O . . . |
$$ | . . . , . x x x x , . . . . . . O . . |
$$ | . . . X . x x x x X . . . . . X O . . |
$$ | . . . . . x x x x . . . . . X . X . . |
$$ | . . . . . x x x x . . . . . . . . . . |
$$ ---------------------------------------[/go]
Black may end up getting more points in the area. By
reducing, white reduced black's potential in the area.
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Invading, on the other hand, is not about conceding points to your opponent. It's about trying to take away points in that area completely, either by living there yourself, or by splitting them up.
For example, it may not be a good move, but this is an invasion, from the same position:
$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . O . . . |
$$ | . . . , . . . . . , . . . . . . O . . |
$$ | . . . X . . . 1 . X . . . . . X O . . |
$$ | . . . . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . O . . . |
$$ | . . . , . . . . . , . . . . . . O . . |
$$ | . . . X . . . 1 . X . . . . . X O . . |
$$ | . . . . . . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Assuming white lives, black won't have many points in the area he did from the reducing variation. For example, assume black plays in a slack and simple way - just to show a simple variation.
$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . 5 . 4 . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . 3 . 2 . . . . . O . . . |
$$ | . . . , . . . . . , . . . . . . O . . |
$$ | . . . X . . . 1 . X . . . . . X O . . |
$$ | . . . . . . . . x . . . . . X . X . . |
$$ | . . . . . . . . x . . . . . . . . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . 5 . 4 . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . 3 . 2 . . . . . O . . . |
$$ | . . . , . . . . . , . . . . . . O . . |
$$ | . . . X . . . 1 . X . . . . . X O . . |
$$ | . . . . . . . . x . . . . . X . X . . |
$$ | . . . . . . . . x . . . . . . . . . . |
$$ ---------------------------------------[/go]
It's hard to say that black has gotten points in the area on the bottom of the board, because white has established a presence there.
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Generally speaking: Reducing concedes more to the opponent - kind of like negotiating. It's like, "you can have this many points here, but that's it. I'm reducing your potential, and you just keep that area.
Invasion, on the other hand, is less about conceding, and more like, "move out of the way. I'm breaking this area up so that you don't get territory here."
You may take away more of your opponent's points with invading, but reducing is safer, since it's less likely the opponent will try to kill you.
There are exceptions to the definitions I'm giving, but to give you a basic idea, this is what I feel distinguishes invasions from reductions.