What is the difference between a barrel roll and an aileron roll?
The difference between an aileron roll and a barrel roll is that an aileron roll's centre of rotation is very close to or on the aircraft. A barrel roll has its centre of rotation around a point further away from the aircraft itself.

The difference can be appreciated in this image:



Image Source You can find out about the difference in feeling that these two manoeuvres have.

Having stated these things, the manoeuvre shown in the GIF is certainly an aileron roll.