jglynn-It depends who you ask...the names folks call coyote dogs varies.
Greyhound=Dog for the track (hotblood) but some call all coyote running dogs "greyhounds"
Staghound=Blend of running dogs (greyhound, deerhound, wolfhound etc..) selected specific for coyotes. Some only call the ones with hair stags, some call any dog used for coyotes stags.
The differance between a stag and a greyhound is like the differance between a top fuel dragster and a Baja 1000 trophy truck. Both fast, but one is alot better in rough ground.
Typically the "stag" has more hunt, and the "greyhound" has more speed.
Take care.