There are established protocols for any incoming emergency call to any of the services, both statutory and voluntary. They of course vary between those services, but there is some commonality of function between them. The reasoning behind them might not be clear to the first-time caller, but once explained it does make sense.
Any information sharing between emergency services, the public and other interested parties needs to be done in the right way, at the right time and to the right people.
This article is not necessarily about dialling 999/112/911, but about how you prioritise the information you are passing along when you do need to call for help.