Your diagram looks like a flat scissors.
FLS, look closer. Notice the F-16s first move is a roll over the top of the red airplane. Later blue "reverses with a barrel roll".
As for a barrel roll being a loop and roll…depends on how you do them. The big loopy one is as you said. Another version is flown tighter, you displace the nose to one side of your reference point and roll "around" that point…IMO the latter is harder to do well….the former is much pretty and fun to fly.
I'm an octoflugeron guy myself.