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).
I would call a cluster a "hot standby". Anything high availability model which "should" require no intervention in the event of failure would a hot standby.
Mirroring with a witness is a hot standyby. Mirroring without a witness is a warm standby.