In the rulesets most used in practice it kida is. The game is finished when the both players agree it is. (I have quoted the rules in another thread). It’s certainly possible to design a ruleset that would not require such an agreement (say, no pass go with prisoner return), but it would probably require making lots of trivial boring moves before counting.
IIRC, area and territory scoring are giving the same result only if it was White who made the last move (as required by AGA rules). Otherwise there is one point difference. That’s if there is no further complications (seki with eyes, etc).
Actually, Chinese rules specify a compensation of 3.75 zi. The entire counting procedure is rather different.
11 Compensation
Official competition uses a compensation system.
When the game is finished, black subtracts 3 ¾ stones
from his total count. For example, if black’s total count
is 185, then black wins by ¾ stone. If black has 184,
then black loses by ¼ stone. If black has 184.5, then
black wins by ¼ stone.