From OED
Cavern
cavern (______), n. Also 4_7 cauerne, 5_6 kauerne.
[a. F. caverne cave, ad. L. caverna cave, den, cavity, f. cav-us hollow: see -ern.]
1. A hollow place under ground; a subterranean (or submarine) cavity; a cave.
The Fr. caverne is the exact equivalent of Eng. cave; F. cave is a subterranean hollow generally, a cellar, etc. In Eng., cave is the ordinary commonplace term, cavern is vaguer and more rhetorical, usually with associations of vastness, or indefiniteness of extent or limits.
and
Cave
cave (____), n.1 Also 4 kaave, 4_5 kave.
[a. F. cave:---L. cava, pl. of cavum a hollow (place), neuter of cavus hollow.]
1. a. A hollow place opening more or less horizontally under the ground; a cavern, den, habitation in the earth.
2. gen. A hollow place of any kind, a cavity.