Really a matter of terminology, but there's a clear separation between underground heavy rail (all of the New York City Subway) and underground light rail. You

Really a matter of terminology, but there's a clear separation between underground heavy rail (all of the New York City Subway) and underground light rail. You can see this division in Boston and San Francisco. Heavy rail has much more capacity, generally has more/larger/better entryways, and has more spacious trains. It might also be faster, although that's possibly just a function of stop frequency.