Life In 19x19

Brilliant responses, thank you! Plenty of new info to digest and another avenue to learn

Ah sorry I should have been more specific, I meant in territory scoring!
Considering filling in the neutrals in territory scoring could change the score, how do players choose who fills in first or where?

Say a game has ended by both players passing, ended by agreement, why are any neutral points of territory filled in when doing this can result in atari or further issues?
Surely in that case the outcome may have been different depending on which player filled in that particular point, so the order ...