Craig: As Nathan explains, most authorities only make a distinction between "pony" and "through" configurations for truss bridges and not other designs. However, on this site, I generally do try to make the distinction for arch bridges, as this makes the design of the bridge more clear.
For girder bridges, it doesn't really matter, although I've always found the term "through girder" to be ugly: it makes me think of the Robert Stephenson "tubular" girder bridges in the UK that do have overhead bracing. See:
The term "through" in bridges means that the superstructure is above and beside the deck. It is not required that there be overhead bracing, with the single exception being truss bridges. As you probably already know, with truss bridges, we use the term "pony" to refer to truss bridges without overhead bracing. While this "pony" and "through" set of terms might seem useful with arch bridges, these terms are not used by those in the transportation/bridge industry with any bridge type except truss bridges, at least in my experience. While I know BridgeHunter often labels through plate girders as "pony" plate girders, this is the only place where I have seen that usage with girders.
By the way, in the old days, pony truss bridges were called "low truss" bridges and through truss bridges were called "high truss" bridges.
This arch is listed as a through arch, help me here, I understand that the roadbed passes "through" the arch with the arch extending above and below the roadbed, but I thought a "through arch" meant there was at least one overhead tying element that connected from one side to the other. I am looking to learn here.