Liquid foundation is just that: foundation in liquid form.
Mousse foundation is just that: foundation in mousse form.
And matte foundation is just that: foundation with a matte finish.
The form is all up to you. You can get it in liquid form, cream form, stick form, mousse form, powder form--there's so many various forms, but it really doesn't matter which one you get, because it's all a personal preference. I personally prefer liquid or cream.
The finish is also a personal preference: there's matte, semi-matte, satin, luminous, and dewy finishes. I LOVE luminous finishes, although I can settle for satin or dewy as well. Matte is a no-go for me, although since you have oily skin, the matte finish could benefit you greatly.