I don't think it has to be, but UA doesn't have both AVOD and DirecTV on the same aircraft, at least currently. They do have movies on the aircraft with DirecTV, but they are not on demand, they start at whatever time, maybe around 15-20 minutes after takeoff, and run on a loop throughout the flight. I think they are stored on an onboard server - since the movies are available even when DirecTV isn't (ie, over the ocean on flights to the Caribbean/Hawaii, etc.).

Just looking at JetBlue, they seem to have both AVOD and live TV - I assume it's still DirecTV. International carriers also have (or had, at least) live tv options as well as AVOD. Turkish is one. Never flown them, but doesn't EK have live tv too?