Airwave is the UK TETRA system. Soon to fail. Airwave is closing its UK sites and network back up, cutting jobs. There are doubts about Airwaves ability to handle high call rates and data. It looks like most of the UK will be going back to analogue UHF and VHF systems in readiness for the whole thing to fall over.
Motorola own the Island TETRA system. Which is a different thing.
TETRA is just the name given to the Truncked radio data system used.