Who on earth gives massage with a powder??
Oils are what they say they are - oils. They're produced by pressing whatever plant material they come from - peanuts, grape seeds, olives, etc. Oil tends to reduce friction the most, but it also does not absorb well into the skin, which leaves the client feeling oily afterwards. Oils are also used to make gels, creams, and lotions.
Gels are basically oils or oil blends that have been thickened with some sort of agent like cornstarch. The advantage is that it usually takes less gel to do a massage than it does straight oil. For clients with a lot of body hair, an oil or a gel is the best choice because creams and lotions usually just knot the hair.
Creams are like light lotions. They feel nice going on, they absorb into the skin very well, but they don't have the glide that oil has.
Lotion is mainly for small areas of deep tissue work where you aren't going to be using long effleurage strokes. It has even less glide than cream has and it absorbs fairly quickly.
I've never heard the term emulsions referred to in this context, but I'd imagine it's something like shea butter that is solid at room temperature and needs to be manipulated or melted - emulsified - into a liquid form in order to be useable.