I know I'm being very general here in using this coin as an example, but I see this obverse portrait (or very similar) on a lot of coins, but descriptions for these coins call it either a portrait of Alexander or a portrait of Herakles, with seemingly no distinction between the two. My question: is this a portrait of Alexander, a portrait of Herakles, or a portrait of Alexander represented as him being Herakles (but Alexander nonetheless)? And, if they are two different portraits, how do you tell them apart?
As far as I know it is largely a matter of interpretation. However when I look at them I see a lot of resemblance between the Alexander Heracles coins and the Alexander mosaic from Pompeii, which is said to be based on original which would’ve been made not too long after Alexander’s death. There is also a Roman copy of a sculpture of Alexander which is believed to have been made during his lifetime called the Azara Herm. (Click to enlarge)
This is the portrait bust I'm familiar with, the Louvre's Roman copy of the portrait bust done by Alexander's favored sculptor Lysippos, so about as accurate as can be expected (I think it's the same one in your second photo):
It's an understandably debated area. Some coins look near exactly as the minds eye figures he looked. And then others are do... Not. Good ol chunky Alexander: Nerd Alexander. At least Lysimachos gave us an image of the defied Alexander! That, and the image of Herakles wearing the nemidian lion had been a very popular motif on coins centuries before ATG3. Muddying the water when trying to decipher who the portrait is supposed to be.
Actually, the portrait of Herakles on the OP coin appears on coins that precede Alexander the Great, so it can't be him on the obverse: https://www.vcoins.com/fr/stores/pr...6328_bc_au_quarter_stater/997673/Default.aspx Whether or not the facial features were modified over time to more closely resemble Alexander is debatable, I suppose, but the portrait varies so much anyway I'd say that question was not really answerable.