In the original Spanish title this is clear—it's called El Laberinto del Fauno (The Labyrinth of the Faun). But because of English and marketing, things got a little confusing…so let's break it down.
Pan is the Greek god of nature, the wilds, and shepherds. He is often depicted with goat hind legs in the manner of a faun (which is where things can get a little twisted) and is associated with music and with sexuality.
In fact, Pan's explicit association with sex is what drove del Toro away from including him in the movie. He felt Pan would be too dark and sexual for a movie featuring an eleven-year-old girl as its protagonist.
The Faun, on the other hand, is a half-man, half-goat creature from Roman mythology with ties to the Greek mythology Satyr. Fauns are very similar to Pan in that they're associated with nature and music and seen as an antithesis of civilization.
Unlike Pan, fauns are less sexual beings. They're more whimsical, often appearing and helping are scaring lonely travelers in the woods.
The point is that anyone who calls the Faun in Pan's Labyrinth "Pan" is technically wrong—although it's hard to blame them. Oh, and also there's a labyrinth. We almost forgot.