I think it done by how much time between landing and fuel runs out. I believe it is 30 minutes. Pilots declare mayday fuel and are given a straight in approach or divert to another airport. This is more common with long haul international flights..
"...straight in approach...". Actually, when declaring an emergency; all traffic is cleared; you are asked what your intentions are; (where do you want to land that Roman Candle?); how many souls on board; how much fuel on board.
You can even do an "Indianna Jones"; and land on a taxiway.