This is confusing.
Subway is already a kind of train.
You mean to say that the train partly runs underground? That is pretty common. I actually can't remember any city where airport connecting train does not do the same at some point or another.
What's kinda interesting is does that train classify as metro transit that goes slightly beyond city to airport and such (making many stops all the way) or distance intercity train that happens to stop both at airport and city? Or does it change this classification? That would be actually unusual.