Perhaps we could find help in the historical context.
When the Metropolitan railway opened in 1863, it was not meant to be a simple commuter short line, rather it's own impressive main line, just mostly underground. It's this mainline distinction which helps to better define the differences from an LRT or tram system. Mainline trains typically have:
- ROW when crossing roads, with no/minimal streetrunning because of the high traffic.
- High entry points, to accommodate platformed stations
- Separated, shuntable carriages
Compare this to a tramway's definable features:
- Priority (sometimes) when crossing intersections, typically running on the street for most of, if not all the time.
- Low entry points, to accommodate stations with minimal/no platforming
- Single, usually articulated, vehicles which cannot be divided like a train's carriages.
With LRT the differences become more ambiguous, and takes aspects from both a typical metro line and a tramway, as the specific need arises. Most always though, you can tell the difference between an LRT or tramway and a metro by the boarding point. It's the underside of a vehicle which makes the difference between light and heavy rail.

(TTC's Wikipedia page)
This is rolling stock from a metro - the boarding point is high, the trains have multiple interchangeable carriages, and it's not safe to run at-grade.

(Confed. Line's Wikipedia page)
This is rolling stock from an LRT - the boarding point is low, they're less trains and more singular vehicles, and the hidden undercarriage makes it safe enough to run at-grade.