So the problem is the term "light rail" and "heavy rail" are really technically meaningless. Historically they referred to how physically heavy the actual rails the trains ran on were because freight railroads used a much heavier rail for their mainlines while interurban transit services used cheaper lighter rails because they almost exclusively ran what would now be called an "electric multiple unit" with 1-3 car trains, thereby not requiring more heavy duty rails

Nowadays the actual rail is far from the largest cost and the operational simplicity of using the exact same grade and standards of rail as the freight railroads means they can move their equipment on the freight railroads' tracks and freight can be moved on their tracks as needed. Because this shift happened to occur during the period of railroad disinvestment in the US nobody really bothered to update the nomenclature so now that we're reinvesting in rail it completely makes no sense at all

Personally I like to use the terms "interurban" for frequent local services with equipment tuned for commuters that runs between cities (and I mean "cities" from a functional definition not a legal one. Just because Shuamberg is legally a separate city doesn't mean it isn't functionally part of Chicago. There really aren't any remaining interurban services that fit this definition in the US anymore) "commuter rail" for passenger rail service within a sprawling metropolitan area and runs equipment tuned for commuters, "regional rail" for passenger service that goes further than a simple commute or a quick run to the store/museum, has equipment tuned for passengers spending more than an hour on the train. And "long distance rail" for passenger services that are tuned for travel of greater than 300 miles. To me "metro" refers to a grade separated urban rail transit system (so like Chicago's L or the New York Subway) and "tram/trolley" refers to a ground level urban rail transit system functions like a higher capacity bus, potentially intermixing with car traffic

But this just demonstrates the problem which is that the US has so disinvested in rail transport that there's no clear, consistent definitions in use anymore so people have to define what they're talking about every dang time!