>light rail
dedicated right of way, tram rollingstock, low platforms, passengers can walk across the tracks more often than with ordinary heavy rail
>tram
a rail vehicle lighter than a train that travels on a road, either in its own dedicated lane or mixed traffic and which is low enough to not need a platform to board
>metro
A train in a built-up area with short stop spacing and complete grade separation from other modes, often in tunnels and bridges.
>heavy rail
A comparative term from light rail, meaning the opposite. Trains with large loading gauge, large trucks and dedicated rights of way (except for the occaisional bit of street running).
>regional rail
Trains that leave major cities and stop very infrequently. Serves areas that don't warrant frequent train service and connects cities together.
>commuter rail
Railways meant to bring passengers from within an acceptable commuting distance/time away into centres of work. Connects the suburb to the city. I prefer the term suburban rail though since trips other than work are important too, like going out on the weekend.
>light metro
medium capacity stuff in between the usual definitions of tram and train. I prefer the term medium rail honestly.
There you go op, different solutions for different problems. Now go ride the bus.