There are a few differences, but they're pretty hard to spot externally unless you've studied both species in great detail. There is a way to tell the two apart but doing so can potentially be life-threatening for the gar if you do it wrong.
IMO, anyone on here who says that they can tell the two apart from just a picture and no other information is probably just making stuff up as there are only two people on here (E_americanus & Polypterus) that I know could give an accurate ID from just a picture of a supposed "spotted gar." Otherwise the point of collection is the best indicator for those of us who aren't quite so good at giving IDs for those two species from just a picture. If it's from a farm, then it's definitely a Florida gar even if the farm says otherwise (as most farms don't even know what species they're breeding); if it's wild-caught, then your chances are far better provided that it's not from certain parts of Florida & Georgia where Florida gars occur naturally.