Basically, there are three types of leases:
1) Dry Lease: a/c is leased - nothing else
2) Damp lease: a/c leased with pilots, but no cabin crew
3) Wet-lease: a/c leased with pilots and cabin crew
These are just the three basic, "generic" leasing forms, but there can be many variations and hybrids; for instance a damp/wet-lease where part of the cabin crew is supplied by the lessor, part by the lessee.
For obvious reasons, the longer the leasing period, the more you go towards a dry lease - a football team that charters an a/c for a match is essentially a wet-lease; financial leases (from i.e. ILFC) are (as far as I know) always dry leases.
"I was waiting for you at DFW, but you must have been in LUV" CPH-HAM-CPH CR9