Is it VA 624, SR 624, or SSR 624? I've seen all three of them in various places.
VDOT in various places refers to all roads as a "route" whether it is a U.S. highway, a Virginia primary highway, or a secondary road. In other places, there is a distinction between "VA Route 16" and "Route 738" although it isn't consistent.
VDOT does designate primary and secondary based on the route number:
"Routes within the Primary System are numbered from 1 through 599
statewide and roads within the Secondary System are numbered 600 and
above countywide. There is no relationship between route numbers and the
direction of the routes.
An exception is Interstate Route Number 664, this number would normally
designate a State Secondary Route; however, it is assigned to an Interstate
Route." (Virginia Route Index,
http://www.virginiadot.org/info/resources/route-index-07012003.pdf)
The AP Style Manual addresses how to identify highways generically, without any specific reference to Virginia. There are some media outlets that will refer to "Va. secondary 735" in a story to give the location of a traffic accident or other incident.
Typically when I am writing directions, I'll use VA 114 for a primary highway and Va. 685 for a secondary route.
Bruce in Blacksburg