Faunus ~ Roman counterpart of Pan. 

Faunus

The god of wild nature and fertility, protector of flocks, agriculture, nature, woodlands, dance and music, also regarded as the giver of oracles.  
He was later identified with the Greek Pan and also assumed some of Pan's characteristics such as the horns and hooves. As the protector of cattle he is also referred to as Lupercus ("he who wards off the wolf").

One particular tradition tells that Faunus was the king of Latium, the son of Picus and grandson of the god Saturn After his death he was deified as Fatuus, and a small cult formed around his person in the sacred forest of Tibur (Tivoli). On February 15 (the founding date of his temple) his feast, the Lupercalia, was celebrated. Priests (called the Luperci) wearing goat skins walked through the streets of Rome and hit the spectators with belts made from goat skin. Another festival was the Faunalia, observed on December 5.

He is accompanied by the fauns, analogous to the Greek satyrs. His feminine counterpart is Fauna. The wolf skin, wreath, and a goblet are his attributes.

 

Fauns

Among the Romans, fauns were wild forest deities with little horns, the hooves of a goat, and a short tail. They accompanied the god Faunus

Merry, singing, dexterous, always having fun time. Fauns are analogous to the Greek satyrs.

 

PAN

The god of woods and fields, of flocks and shepherds, dwelt in grottos, wandered on the mountains and in valleys, and amused himself with the chase or in leading the dances of the nymphs. He was fond of music, and was the inventor of the syrinx, or shepherd's pipe, made from the transformed body of the nymph Syrinx, which he himself played in a masterly manner. Pan was also a god of fertility, unbridled male sexuality and carnal desire

As the name of the god signifies all, Pan came to be considered a symbol of the universe and personification of Nature; and later still to be regarded as a representative of all the gods and of heathenism itself.

 

Satyrs

In Greek mythology the satyrs are deities of the woods and mountains. They are half human and half beast; they usually have a goat's tail, flanks and hooves. While the upper part of the body is that of a human, they also have the horns of a goat. They are the companions of Dionysus, the god of wine, and they spent their time drinking, dancing, playing music, and chasing nymphs. The Italian version of the satyr is the faun, while the Slavonic version is the Ljeschi.