Hey there. The one on the left looks like Hadrian, and the right might be PIUS or Aurelias. They are both 18mm wide (basically the size of AE3). I don't know how to even search for greek lettering on coins, so was hoping to get some help on ID, thanks!
The one on the left is Hadrian as you surmised. It was struck in Gaza. The city name is clear on the reverse as emphasized here: The standing personage is mythological. A search on a coin venue (perhaps ACS or similar) will easily take you the rest of the way toward an attribution.
The coin on the left is the equivalent of a Roman semis, minted in Gaza under Hadrian in 134/5 CE (RPC III 4041). On some dies used in this coin emission, the reverse legend is a little blundered. We read ΓΑΖΑ Ε ϚΠΙ EЧΡ presumably for ΓΑΖΑ Ϛ ΕΠΙ EЧΡ. It means "Gaza, (year) 6 of the Epidemia (the imperial visit), (year) 195 ". Roman Gaza used a local era starting on 28 October 61 BCE, when the Romans restored the independence of the city. Gaza had been taken by the Jews in 98 BCE and was submitted to the Jewish Kingdom, until Pompey took control of the Near East and restored the liberty of many Greek cities including Gaza. The city used this era starting in 61 BCE during all the Roman, Byzantine and even the early Islamic period: a church mosaic found in Gaza is dated 792, that is 732 CE, under the Umayyad caliphs... The "year of the Epidemia" is another special local era starting from the official visit of the emperor Hadrian in the summer of 129 on his way to Egypt. Gaza, who had not minted coins since Vespasian, was granted by the emperor the privilege of minting a whole set of 5 bronze coins like Rome itself : sestertius, dupondius, as, semis and quadrans. These coins were dated according two eras : the city era and the era of the Visit. This one is a semis dated 195 / 6. They stopped using the "era of the Visit" after Hadrian's death, all later Gaza coins are dated with the city era only. In the left field there is an Aramaic letter : mem (a M). All Gaza coins since Hellenistic times have this mem somewhere on the reverse. Its exact signification is not known, probably the initial of the city supreme god Marnas, but I don't like this explanation because no document mentions this god Marnas before the time of Hadrian, and this letter was already on Gaza coinage since the 2nd c. BCE, perhaps even in the 4th c. BCE... The deity represented on the reverse is Heracles standing facing head right, leaning on club and holding lion-skin.
Thank you both so much. I learned a lot by reading your responses and really enjoyed myself. I never put together that, at the time, there wasn't a wholly accepted calendar.