Hot standby is a server that will automaticaly failover if the primary server fails. You can get this using synchronous mirroring + witness (not sure if a cluster can be called a hot standby).

Warm standby is a server that will not automaticaly failover and that may not have all the latest transactions. You can get it by using log shipping or asynch mirroring.

Cold standby is just a spare machine that needs to be turned on, backup restored (or even full staging of the machine).