I think there's a bit of confusion on the name. Cupressus glabra seems to be a synonym of Cupressus arizonica var. glabra according to the plantlist: http://www.theplantlist.org/tpl/record/kew-2748665 . I also think some of the names in PlantFiles need to amended. I agree with Resin and RosinaBloom.
The plantlist is out of date there, recent genetic analysis has shown that Cupressus glabra is less closely related to C. arizonica than first thought, so it is better treated as a species in its own right, not a variety.
C. arizonica differs in less glaucous foliage, subtle differences in cone shape, and 'stringy' textured bark (smooth / scaly in C. glabra).