what are some other words like deserts/desserts??
Dessert = pudding, sweet, afters (when used to describe the final course of a meal). I think the 3 examples I've given are more typical of BrE than AmE, and some of them would depend on what part of the UK you come from.
Desert - I don't know any other words for desert! A desert is a desert. Sahara Desert. Gobi Desert. Yes, it's a vast expanse of sand-covered land, but I don't know one other single word that can be used in its place.