This is where having the OnX map on the computer AND using the DeLorme atlas can help.
"Usually" if it is a road with a name or number, it is public.
2-tracks that are established and are on public land are OK to use. You're not supposed to venture off from them, however.
Roads that cross private land are often posted if you're not supposed to use them. Unnamed roads on private land are always private.
Generally what you see on the Chip is accurate, and I've seen it specifically mention private roads.