Well there's several levels of priority interpreted when dealing with ATC - at least here in the US. The lowest would be asking for priority from ATC for something like approaching minimum fuel. Not an emergency, but telling ATC you don't have much room for any delays or penalty vectors. If a pilot declares emergency, that means they need to get on the ground immediately with no delays. Sometimes you here airline pilots use the emergency phraseology when they get at minimum fuel in busy airspace. They need to have time to complete an approach and possibly go around without further holding or delay. Pan-pan is the international version of declaring an emergency that requires priority. Mayday would be the ultimate distress call, and would almost always be used by any pilot that's in a life threatening situation likely ending in casualty.