The outer layers of gray matter in the brain are called the cerebral cortex. Gray matter structures below those outer layers are called "subcortical". Subcortical structures include the caudate, the putamen, and the thalamus, among others.
People will sometimes say that the hippocampus is a subcortical structure too, but that's not quite right. It's continuous with the outer surface of the brain, so it can't very well be subcortical. It does have a different cellular structure than most of the cortex, which is where people get confused. (Technically, it's "allocortical," and most of the rest of the cortex is called the neocortex, but that's only if you want to be anal.)