UNF = Unified Fine, which is what I've found people here in the US often call SAE or Standard Fine. Anyway, it's the normal American fine thread.
BSF = British Standard Fine, which is what was the standard fine thread in Great Britain and a few other parts of the World (where they weren't Metric)until just after WWii, when UNF was adopted to make exchangeability easier.
You might also find:
UNC = Unified Coarse, the standard coarse thread you find in every US hardware store.
BSW = British Standard Whitworth, the old standard British coarse thread.
BA = British Association,a fine thread standard used mostly for smaller sizes and common in electrical and carburation systems.
BSP = British Standard Pipe, used as the name implies for certain pipe connections.
All of the above differ in one or more ways, be it in thread pitch or form, and have differing head sizes. The significance is that you need several sets of wrenches, sorry, though generally one set for BSF and BSW, one for UN threads, and a few small ones for BA.