Well its kind of funny actually, because curing and cycling are sort of the same thing. Basically putting the rock in the tank, providing light, heat and water movement to wait for various things to finish dying (induced by transport etc) and breakdown by bacteria etc. Curing and cycling are both done using light usually. That way stuff that is decomposing continues to do so and coralline algae can take hold and proliferate.
However, technically I suppose rocks that are to be "cooked" are already "cured/cycled" (ie. they have the bacterial populations to keep nutrients in check).
I guess someone thought they'd come up with a trendy term called cooking (which also conveniently starts with "c", not very original IMO). Kind of silly since you're not really cooking anything. Although in my world it could be termed as cooking: add water, heat and then forget about it for awhile. Thats how I make Kraft Dinner
I've been tempted to boil my rocks a few times. Some of these critters we get on the rocks are unbelievably tough (ie. hydroids, turf algae). Its only the possibility of stinking up the house that has stopped me.