"Gargoyles are statues.

Grotesque is a word meaning very ugly."

NOTE: This answer is incomplete and seems to have been answered by someone who didn't realize that the two items in question actually have a historical similarity.

Grotesque does of course mean ugly but it is ALSO the name for those varieties of stone statues that are found on buildings such as old cathedrals - and which usually take the shape of an ugly mythical creature, such as a griffin. Grotesques are commonly confused with Gargoyles but they are in reality very different. One serves a function and one is purely decorative.

A gargoyle by definition differs from a grotesque because gargoyles are actually rain spouts. The mouth acts as a spout for a gutter system that passes water flowing from the roof top, into a trough, and lastly, out of the mouth of the statue. A gargoyle can be in the shape of any creature, ugly or not. The ugly ones are the most common but some gargoyles are in the likeness of angels.

Most statues that are commonly thought to be gargoyles are actually grotesques because they do not serve as gutter spouts and are merely decorative.