1.) arbalest= Historically a term for a rennaisance era crossbow using a metal as opposed to wooden stave. Are you talking about the siege engine the PHB calls a ballista and the romans called scorpions?
2.) heavy/military crossbow=Not the kind of crossbow you can pick up in a sporting goods store, but the special forces still use modern versions occasionally. They have a very heavy metal stave and use metal cable rather than typical bowstring with a draw of about five to six hundred pounds and a winch for drawing them, accurate to about 150-180 meters.
3.) light/hunting crossbow=Basically you can pick up more modern versions of these in most sporting goods stores. Not really accurate beyond about 60-90 meters depending on the wind but that's because they've lightened the bolt too much until its more like an arrow and wind affects it more.
4.) english longbow=WELSH WARBOW, the english just stole the idea when they realized it worked. Damned good bows for the time and purpose, accurate on single target to about 50-60meters and mass targets significantly farther as much as 300 meters in favorable wind conditions with heavy draws. Was not fired like most people figure, they were held diagonally when fired at about a 40 degree angle across the body. Once you get used to the posture and the difference in aiming it solves most of the problems with shooting such a long bow at short ranges and seems to improve yawing in crosswinds a bit.
5.) recurve bow=most bows you see today that aren't compound are recurves, they do a good job of packing more power into a shorter stave. Not really that accurate beyond about 50-60meters on point targets.
6.) short/self bow=roughly same size as recurve but without the extra curve, not as powerful for the length and run into the same limitations as all bows at about 50-60meters on point targets.
