Folks behind the desk at the Jackson office wouldn't know much about that.
aside from size:
Muleys: big ears, carried at a distinct angle. tend to appear floppy.
antlers fork
faces white between nose and eyes. both muleys and whitetails have a white path under chin
They tend to stot when alarmed- bouncy gait with all four feet
Whitetails: smaller ears, carried more erect, especially does
antlers are main beam with points rising
faces brown between nose and eyes
tend to gallop when alarmed. Tails flag when alarmed. big white flag when they move away from you, that's a whitetail
All in all, whitetails are more brown, muleys get quite grey by October around here.
I've seen plenty of whitetails in recent years around Jackson, but my feeling is that they tend to be lower, in heavier, wetter cover. Muley's like drier, steeper, more open ground. I can't recall seeing a single whitetail around this valley above 8000'.
Muley's like to go up. If you can get above them you can make them hesitate. Whitetails will run circles in the same patch of cover.