'Freeway' is a regional term, but the Federal Highway Administration describes them as limited-access with directions of travel separated by a barrier.
Yes and I believe when OP said highway they meant it colloquially, as in a freeway, hence using that term in my reply. A highway wouldn't really make sense since it encompasses just about every road, as you say.
https://www.fhwa.dot.gov/planning/processes/statewide/relate...
The Federal definition of highway is basically any public road.
https://www.ecfr.gov/current/title-26/chapter-I/subchapter-D...