You’re saying pretty much any non-private road is a highway.
I’ve always differentiated between freeways and highways.
Freeways have on-ramps, not cross streets, no stop signs or red lights.
Interstates are freeways.
Note that as per your number two interstates or freeways are not highways. No foot-passengers or beasts of burden.
All freeways and interstaes are highways, not all highways are freeways or interstates.
That’s just the definition. Usage varies by region and personal background. In Connecticut, where I grew up, the common description for the Interstate is “Highway”.
Per Co-Pilot AI:
The official name of the U.S. Interstate system is the Dwight D. Eisenhower National System of Interstate and Defense Highways. It’s often simply referred to as the Interstate Highway System or Interstate System. Named after President Dwight D. Eisenhower, who championed its creation, the system was designed to facilitate efficient transportation across the United States and provide critical infrastructure for national defense.
So, while the term Interstate is more specific, “highway” is completely accurate.