Very easy to tell. If its BGA, it should look slimy and if you take it out of the water it should stink something awful. If its hair algae, it should look look either brown, green, or grey, and looks very soft because each of the hairs are so close together they form a mat. BGA is normally caused by very low (or no) nitrAtes, hair algae (if you mean BBA) can be caused by several things but normally results in low/fluctuating CO2 levels.
I would wager a guess if you have fish in there and small/low numbers of plants but good water circulation its probably NOT BGA (since there are probably nitrAtes) and more likely BBA, but without pictures we're guessing. Either way you need to fix the fert issues.