There’s both a rail and Metrolink line from the Airport to Town.
The railway from the Airport goes to Piccadilly.
The Met from the Airport goes to Victoria.
You have to change Mets to get to the Etihad and no trains run out to the Etihad.
As you can see here though, the Airport Metrolink line slaloms and snakes through the South of the city, side-to-side, which makes it a very lengthy journey for the A-Z journey you’re actually doing:
View attachment 35386
But all the other Met lines are really bloody slow once you hit Town anyway, because you hit roads and pedestrian areas. It’s waking pace through some areas of Town on the Met, it’s
ridiculously slow! (The City Centre should have been underground, but that’s another matter altogether!)
So, opt for the train to Piccadilly and jump in a black cab to the Etihad if you’re coming from the Airport.