This is also rail terminology here, wouldn't have used it otherwise. But from the rest of your reply, it appears to me that I still failed to completely convey what I meant. What I meant (and spelled out upthread, maybe not in the clearest way) was exactly this:

the very high speed rail should take the most rapid route between the centers that it is connecting, and the medium high speed rail should take the route that provides the most effective transport for potential passengers at the intermediate stops in between

I.e., I meant separate alignments between two major cities, which can get dozens of kilometres apart, one new and straight and avoiding smaller cities, the other an upgraded old line crossing smaller cities. To expend money on smaller-city-traversing high-speed alignments, or worse on parallel high- and low-speed lines, and have two types of service along the same line, makes sense only when population density is high anyway and concentrated along a narrow strip -- e.g. like Japan's West Coast, Taiwan's East Coast, but also the US Northeast Corridor (as in Marek's proposal).

And of course there are a lot of existing alignments in the US that are not fully built out that fill the bill for a medium high speed alignment

I would count only Washington-NYC(-Boston) and a few shorter stretches. I assumed upgrades to the existing lines, including cutoffs and tunnels, not simply different use.

_{*Lunatic*, n.
One whose delusions are out of fashion.}