The "highway" term seems self-explanatory bug a bit confusing. In the US sense, it seems to define roads that are main arteries for long-distance travel but not necessarily freeways. Example: the famous Pacific Coast Highway.
I found highways in the US that are pretty close to freeways with off-ramps and median, and others that cross cities like streets.
The confusion comes from being used to roads in Europe. For instance, in France, there are "nationales" which are main roads that cross the entire country and often follow a similar-named "autoroute" (freeway with median). Such nationales do have divided sections and slow crossings of towns; it varies. Then there are the "départementales", road maintained by the "département" (administrative subdivision of second level), that may encounter the same characteristics as nationales altough divided sections are less frequent. From all those, I do not know which ones could be named as highways.
Also, when talking about car fuel efficiency, there often are city and highway measurements, the highway measurement being often better for obvious reasons. Thus, seems the idea of highway also means faster average speed.
Then, is designing a road as highway based on:
- the type of road infrastructure?
- the authority that maintains that road?
- the importance of the axis?
- the average driving speed?
- some other criteria?