Satyrs - demons of nature who appear in Dionysus' train. They had appearance of half men (the upper part) and half animals (either horse or goat for lower part). They are often depicted as drinking wine, dancing, chasing Nymphs. Marsyas was a Satyr.
See: Albrecht Altdorfer Landscape with Satyr Family.
Pietro Perugino. Apollo and Marsyas. Raphael Apollo and Marsyas; Titian The Flaying of Marsyas.
Silenus - a general term applied to old Satyr. But it is also a name of a character who had brought up Dionysus, Greek Olympian god of wine. Silenus usually described as ugly, with snub nose, thick lips, gaze of a bull, and very fat. He is often drunk.
See: Karl Brulloff Silen, Satyr and Bacchanals.
Anthony van Dyck Silenus Drunk.