The demo contains the first hour or so of the game, the story introduction and a single destination and one enemy type.
The full version has several hours more content, two more destinations to visit, a bunch more lewd scenes, the first 'act' of the game's story, a gallery for reviewing scenes, etc.
If you want to give the story a trial, or want to get some practice with the controls before playing, the demo is a good idea. But otherwise, the full act one is a much more content and feature rich experience!