In architecture, a gargoyle is a carved stone sculpture designed with a spout to direct water from the masonry of a building. They were commonly used in Medieval times, particularly on churches and other tall buildings where erosion of the mortar between stones could cause the collapse of a building.
Gargoyles, often hideous representations of dragons or griffins, were mostly mythical beasts used as a protection against evil. The word Gargoyle is derived from a French word meaning throat or pipe, and also from the root word Gar (to swallow) which represents the sound of gurgling water.
Grotesques as the name suggests are also hideous sculptures but with no practical application other than a decorative role to ward off evil spirits, and as an encouragement to attend church to avoid demons in Hell. The most common grotesque is a Chimera (a creature created from the parts of other animals). Grotesques with wings were believed to fly at night, chasing evil spirits while inhabitants of the town slept.
In opposition to the original intention, the ‘grotesque’ appearance of these sculptures led people to believe that the sculptures themselves were evil.
For more information, read http://www.kuriositas.com/2012/08/gargoyles-glorious-gruesome-grotesques.html