Is there such a thing as medium passenger trains?

Question

Where the medium sized train can travel safely on regular railroad lines.

Answer 1

Sure, there's a size between a full size passenger train (Amtrak) and a "light rail" streetcar (Sacramento, Philly  subway-surface, Portland MAX etc.)

But it's not called "medium rail"... not sure of the name.  But think, like, Budd RDC cars, South Shore trainsets, etc.   They're collision-rated to mix with full size passenger and freight trains, but they're commuter style "multiple unit" cars, i.e. without locomotive.

Answer 2

Yes.  It's called the LRT.  Light rail train.