Tinstaafl, in the UK, irrespective of what a pilot reports to ATC, the controller declares one of seven levels of emergency. The words below come from the controllers bible (MATS Part 1):
5.2 The following terms are in general use but individual variations and extra terms may be found in local emergency orders.
5.2.1 Aircraft Accident/Aircraft Accident Imminent
When an aircraft accident has occurred or is inevitable on, or in the vicinity of the aerodrome. (At some units Aircraft Accident covers both situations).
5.2.2 Aircraft Ground Incident
When an aircraft on the ground is known to have an emergency situation other than an accident which requires the attendance of emergency services.
5.2.3 Full Emergency
When an aircraft is known or is suspected to be in such trouble that there is danger of an accident.
5.2.4 Local Standby
a) When an aircraft is known or suspected to have developed some defect, but one which would not normally involve any serious difficulty in effecting a safe landing;
b) When an aircraft is to be searched following a bomb warning;
c) When an aircraft requires inspection by the aerodrome fire service.
5.2.5 Local Standby (Weather) or Weather Standby
When weather conditions are such as to render a landing or take-off difficult or difficult to observe (e.g. strong crosswind, poor visibility, ice or snow on the runway etc.).
5.2.6 Local Standby (Royal Flights)
When a Royal Flight is landing or taking off.
5.2.7 Domestic Fire
Any fire:
a) on the aerodrome, not included in the categories above;
b) outside the aerodrome boundary (other than an aircraft accident) which is liable to constitute a danger to flying or aerodrome property;
As the good book says, there may be some local variations but these are normally more specific criteria for declaring a paricular level of emergency or additional categories.
BTW, the controller can declare an emergency even if the pilot doesn't declare a PAN or MAYDAY (or even if the pilot doesn't say anything).
[Edited coz I can't count]