You are correct
Game Over is something that depends on the game. Outside of RPG you would think of Game Over either as the fact that you can't continue with the game as a player (some card or board games), you lose some of your progress but can try again (Video games with saves) or have to start over from scratch (saveless video games). The social contract, or shortly an understanding that you make at a table with your players, defines which of these can happen, but some games handle Game Over better than others, while some discourage it completely.
In some games a Total Party Kill is often accepted as a sort of Game Over situation - since no characters survive, players lose significant portion of their achievements and even if allowed to continue, they can do so only with fresh characters. There can also be situations where player-generated failure forfeits their control of their character, e.g. in Cthulhu games losing all Sanity often means the character is a blabbering lunatic and no longer under player's control.
However, other games discourage situations like that by establishing that PCs can't die or that failure is a setback, not a Game Over.
Anima Prime discourages Game Over situation strongly
From Anima Prime PDF:
PCs don’t die when they are defeated. In
fact, there is nothing the GM can do to
kill off the PCs. They are never going to
die because of an unlucky roll, a bad
tactical decision, or the failure to figure
out the trap that the GM put in place.
Accidental character death like that goes both against the spirit of spontaneous fun and against the types of stories that you’re
creating with this game.
p. 55, on Conflicts
The book goes on to explain that characters can only die (or be permanently out of play) by player's decision to sacrifice themselves in order to achieve a heroic deed, save the day and be remembered forever.
In general, if a goal is not achieved, the
status quo remains in place. If the goal
was to rescue someone and no one achieved
it, that person is still captive. After
the conflict, the GM rules whether unresolv
ed goals can still be achieved (maybe
in a follow-up character scene) or, if not,
how they turned out.
p. 58, on Goals
That means even if your players do not achieve their goals in a conflict, the status quo remains - which means they can regroup and try again. Sometimes specific the goals are no longer appropriate or realistic, e.g. if you wanted to stop the bomb from going off and failed, it exploded and there is no way to change it. The plot progresses as the story demands, but the players are still involved in it and capable of achieving overall success - they've lost a battle, not the war. Even if they lose in a final showdown with the Big Bad, it would simply mean it wasn't a final showdown after all, but a setback on the way there. Sure, it means complications and more difficulty ahead, but that's what the game is about.
You might want to consider setting up Enabling Failures, situations where despite the failure, players have avenues of action to explore. Let's say that your characters wanted to catch a thief red-handed. They failed and the thief ran away. The goal is no longer attainable, there is no retry button to press. You can turn this around into an Enabling Failure by putting hints for the players - maybe the thief lost a business card players can investigate? Maybe there is enough evidence on the scene to identify the thief? Maybe something else happened to restart the PCs on their way to victory?
So how do we stop playing?
Some scenarios in games can be effectively finished (e.g. Gehenna stories in Vampire the Masquerade or any other kind of End of The World scenario) without failing, because some circumstance made the current game scope irrelevant (e.g. PCs are gods now, the world has ended, characters have achieved omnipotence etc.). In general, however, most groups have a limited time or desire to play, so after a while you might decide that the story has run it's course and settle that the next game session is going to be the last one. Usually, it means that the players confront the Big Bad and wrap the story up. At that time, when everyone agrees that they are done playing, you roll credits and have the true Game Over.