what is the difference between the free and paid versions
From the description:
The free version of the game on this page is the full game but with some removed features and censored sex scenes.
In the full version, you get access to additional features like uncensored art and the gallery (CG Gallery, Music Room, and Scene Viewer).
So, in the free version, you're free to go through Date an Otter and experience the story but every sex scene is censored and you won't be able to use the gallery to keep track of your progress and view unlocked art, music, and replayable scenes.