If the "road" requires 4wd I consider it "off-road".
The off-road riding that I prefer often requires a saw, and new knobbies.
If you're "unsure" whether what you are riding should be considered "off-road" or not, it's Not.
I generally consider "logging roads" to be off-road, especially after a season or two of erosion.
There are a few un-maintained state roads around here, which are on maps, that are 4wd roads and do require a chainsaw at times. One that comes to mind is "White Oak Rd" near Watauga Lake, just off Hwy 321 in TN.