I have already talked about the second coin type illustrated above. It was produced by Pyrrhus and is said to represent his claim to have Achilles as an ancestor. Thus the obverse is usually identified as Achilles.
The top coin is a Roman didrachm (RRC 25/1). There is a another series (RRC 27) that is usually dated a little after with a similar head:
The Roman coins are invariably identified as Mars. The logic is really no more complicated than this: Helmet = War Deity –> Male War Deity = Mars. This Mars just happens to be beardless as compared to earlier bearded Mars:
[This is by our best reckoning the first silver Roman coin.] Or late bearded Mars like these beauties:
But if we go back up and look the ‘beardless Mars’ of the Roman coin and the ‘Achilles’ of the Pyrrhus coin, I think you’d agree we’d be hard pressed to actually claim there is any iconographic difference. They match pretty well in their rugged Hellenistic faces and even share the gryphon motif of the helmet. We need not make too much of that. Gryphons appear on Corinthian helmets in this position on and off in Hellenistic coinage, regularly enough that we don’t need to attribute special significance to it. Here’s a specimen from Syracuse. And a gold Alexander stater of Sidon.
Are the two separate identifications warranted even with the close iconography? Probably. The Achilles attribute rests on the Thetis image on the reverse and the mythical connection. If Rome copied the image or they simply share some common prototype there is no reason to think that it would be mean anything other than male war god, i.e. Mars to a Roman audience.
Update 2/5/2014: A. Burnett, The Iconography of Roman Coin Types in the Third Century BC. Numismatic Chronicle 146 (1986) 67-75:
Liv Mariah Yarrow 