In my experience, these phrases are used in the following ways:
1. "fill in" the blank, your name, etc. (used with forms, more specific)
2. "fill in" the form, etc. (used with forms, more general)
3. "fill out" the form, etc. (used with forms, more general)
4. "fill up" the glass with water, etc. (used with liquids, quantity of items, etc.)
As you can see, "fill in" and "fill out" are basically the same. "Fill up" is different.