Path is somewhat abstracted in my mind, sorry if that was confusing. 
This is how I see it as I trying to think in OSM semantics. The path consists of a mix of a physical trail one can see and markers that one can see (or not) - that is the abstraction I was thinking about. Caveat: I’m not an expert OSM user, though I do spend quite a lot of time in the backcountry/wilderness especially off-trail and have been learning as I make corrections to OSM as I encounter them in the field.
I’d say the route is the most abstract - it’s like you say someone trying to get from A to B regardless of what form that takes.
One of those ways can be a path. That path can consist of a physical trail (which may or may not be visible, on a spectrum) and/or markers (which may or may not be present at all, and if they are visible on a spectrum). You can have a path without a trail, or a path without markers, or a path with both. A path without both (or with both that are severely degraded due to being abandoned, damaged, overgrown, etc) would in my mind just be a “route” where people having to use advanced self-orienteering aka pathfinding aka finding your own path because none exists in any meaningful real world sense even if you are still trying to get from A to B and there was some path that went from A to B 40 years ago.
At this point we can have a highway=path with trail_visibility=excellent that has no visible path/trail at all because there are bright tall markers every 10 feet (think long runs of posts/cairns/markers on sandstone or granite slabs). In this case the path is abstracted aside from the actual markers, as people have to visualize it in their minds and follow that visualization.
I don’t agree this makes trail_visibility intuitive, but that’s how I understand it.
edit: added the second half of this comment. ^^;