The nomenclature of egg-milk mixtures has always been loose. The English "custard" began as "croustade" in medieval times, and meant dishes served in a crust — thus, for egg-milk combinations, usually baked and unstirred, and so solid. Early English creams could be either liquid or solid, as could the French cremes. Those congealed past the point of creaminess became known as cremes prises, or "set creams."
Flan, a French word, comes from the late Latin for "flat cake."