In the UK, if a flight is being conducted that is being operated by a standard company (so not Helimed) then the area and terminal control controllers have a free text field on their flight details that will say either "MEDIVAC" or "STS/HOSP". I will routinely ask on first contact if they are operating an active hospital flight and alert the next controller if so, aiming to get a short cut etc. A couple of the companies who regularly fly such flights are very switched on and can give us the detail required, either "time critical flight" or "positioning for a time critical flight" can often be said. I'm sure other controllers see and hear other tings too, these are just what I can remember myself.