As nouns the difference between cove and grove
is that
cove is a hollow in a rock; a cave or cavern while
grove is a small forest.
As proper nouns the difference between cove and grove
is that
cove is a town in Arkansas while
Grove is {{surname|habitational|from=Middle English}} for someone who lived near a grove.
As a verb cove
is to arch over; to build in a hollow concave form; to make in the form of a cove.