The two are connected, yes.
The SERV light isn't because a service is due, it is because something is wrong with the car, but it is not so urgent that you must immediately stop.
It can be linked to various things, it is usually accompanied with another warning light on the dash, or an oil low warning on the trip computer. If nothing else is lit up, just the SERV light, I suspect it might well be that someone has tampered with the Airbag light so it doesn't illuminate.
A common problem is the connectors under the seats - usually a wiggle is enough to turn the light off again.