a short education in whips -- three training photos of Thomas Ritter, from his website classicaldressage.com, presumably copyrighted and used here for educational purposes:
"crop" or "bat" -- a short whip carried while riding to to get the horse's attention -- like cher in "Moonstruck" -- "snap out of it!" or "hey, you -- there's a big fence coming up and maybe you should check it out before we go over it." This is used mostly for jumping or hacking out (aka trail riding), as it's not really much use in guiding the horse.
"dressage whip" -- longer than a crop and used while riding to help guide the horse, for example tapping behind the rider's right leg to reinforce the rider's request for the horse to move its right leg sideways under itself. or pressed against the horse's shoulder as a barrier if he's popping that shoulder out and avoiding proper bending in a circle.
Driving whip - well, used for driving. called long line work when the horse is not attached to a vehicle. it's very useful training even for saddle horses -- mine all drive, but without being hooked up to anything -- and you need a whip to be able to touch the horse on the flanks or legs since you're not on him and otherwise only have the bit as a connection:
in hand whip -- used to work a horse in hand (this is different from driving on the ground). very useful to help the horse learn something new without having to deal with balancing a rider on it's back , and very much used to teach horses upper level movements (you can't see the whip here, but he's got one that's longer than a dressage whip and shorter than a driving whip.)
longe (or lunge) whip -- used for working the horse on a long rein on a circle around the handler. it's about 5' long and has a long thong attached so you can reach the horse, for example to touch (gently!) his lower leg and say "please use your left leg better and don't just shuffle along." the horse learns to respond to whip signals, such as raising the whip for "more effort, please" or pointing at the shoulder for "please stay out on the circle without cutting in"