I guess it depends on who you talk to as to what definitions you will get for these, but here is how I interpret them.
Partnership - 2 companies engage in a mutually beneficial arangement where each has equal control.
Affiliate - 2 companies engage in a relationship where 1 drives business to the other in exchange for a fee (or percentage of the profits)
Sponser - 1 company gives money/services/products/help to a second company in exchange for advertising (or just about anything that isn't money).
