From my knowledge (I could be a bit misguided myself though, I don't usually sell too many beats):
When you lease a beat you retain all rights to the beat. You can lease a beat as many times as you want, which kinda sux for the artist. Say you have "Beat 1" for sale or lease, lease is $200 and exclusive is $1500. Now say a cat doesn't have the money to buy exclusive rights and he wants to lease it, yall will make up the contract sign it and he'll give you $200 and you'll give him the beat. Now you can stipulate this beat will be leased
X amount of times. So you can lease the same beat
X more times for however much you want.
With exclusive, the beat is sold once and can not be resold or leased to another artist. So if the artist gives you that $1500 for exclusive rights your beat is off the market after the deal is done.
That's just my understanding of how it works, there also can be numerous stipulations like album points etc...
Don't hold me to this though noddy, I could be flat out wrong. I usually just give beats to people I know and they'll buy the beer