Whilst this might be a simplistic 'rule of thumb', I'm afraid that there is no simple and correct answer. The response to either type of call will depend on a wide range of factors including, for example, the controller's perception of the severity of the problem, the local instructions for ATC, the emergency procedures (if you're at an airport) and the resources that are available to be called on.
In practice, an emergency call (whether on Mayday or Pan) will be assessed by the controller and the appropriate level of response called. The controller typically has about six levels of emergency that can be declared, and will be guided, firstly, by local instructions, secondly by knowledge and training, and finally by professional judgement. This can mean that the same call can result in different levels of emergency service response depending upon other factors. As an example, a precautionary engine shutdown in daylight on a nice day without any other problem indicated may not get the same response as the same problem on a wet and windy night.
More and more, however, the judgement element is being removed from the equation with local instructions specifying, in detail, what level of emergency should be declared for every conceivable emergency aircraft might have. This perhaps leads your checker to imagine that there is a fixed response to every problem reported by a pilot.
One last thing that I should point out is that this is a UK-orientated answer and that maybe other places work a little bit differently.
Last edited by Spitoon; 12th Dec 2009 at 17:45.
Reason: Spilling