It is indeed a Roman Provincial coin of Caligula, from the city of Philadelphia (the city in what we now call Turkey, which the American city was named after), with his name in Greek (GAIOS KAISAR) around the portrait. So the portrait is certainly supposed to be that of the notorious emperor himself.
How photo-realistic or life-like the portrait is, is another question. As noted in the previous thread on the subject, the provinces didn't seem to have been sent an official portrait out to them; they knew the emperor's name but not necessarily what he looked like. A quick browse of the Caligula portrait coins on Wildwinds shows quite a wide variation in the emperor's appearance. This portrait looks much more like a young Augustus or Tiberius, than Caligula; I'd presume the die-cutter in Philadelphia made a best-guess for his portrait, knowing Caligula was related to the previous emperors.
They at least have got Caligula's curly hair correct.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis
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