The possibility that it had been set as jewelry piece would explain the differences in 'shape'.
The reverse has been filed to make it a good fit into some sort setting.
It could be a real drachm although the portrait is much more detailed on the lion skin than I am accustomed to seeing and I remain sceptical. But these are not really my strong area. Best possible assessment I see is someone took a real beauty of an Alexander and "schmucked" it up good with a file ...... making it worth around 80% less than what it might have been.
Worst case is they used a better quality fake to do same.
Not too many decades ago dealers at large International Shows would have bowls full of VF/EF Alexander drachms priced at $40 a pop ! Prices have gone up considerably ...... unless of course someone took a file to it !