There is also a safety element to this; by identifying the aircraft type specifically then there is less potential for confusion.
If I say 'give way to the British Airways A320 from the right' then it's pretty obvious which aircraft I want you to give way to.
If I say give way to the 'aircraft' from the right, and there's one that has just crossed your nose, and another one approaching from off to the right and one coming from the left, which one do I mean? I might have made a left/right error and mean the one off to the left, or I might mean the one off to the right, but I might also assume that you can't see that one and actually mean the one in your 12 o'clock that had come from the right.
At the end of the day, if you don't know the type mentioned, tell ATC that and they will use other information to identify the traffic to you.