There are 8 different story mode endings to Catherine, based on the many choices that the player has made during the course of the game, and some very major ones at the end of it.
There is a 9th ending if the player unlock and completes all the Babel trials.
Each ending completed will unlock one achievement . Completing all of them unlocks a final one.
Once you’ve completed the game and start a new one, you are allowed to skip any puzzle sections that you received a gold prize on, allowing you to quickly obtain all endings. You can do this by pressing “Start” during the puzzle you wish to skip, and choosing “Skip.”
Here is a spoiler-free guide on how to obtain all endings. The True Endings are extended versions of the Good Endings, difference being alternate cut scenes after the credits (and additional achievements).
NOTE: The answer given in Stage 9-1 does not matter.
Catherine All Endings Table