Two people can both say "cyclic" and mean different things. Push the stick forward in both helicopters, then let go. Watch what each one does with a centred stick.
Stick position sets the target angle. Centre stick and the heli returns to level.
Stick position sets how fast the angle changes. Centre stick and the heli holds whatever angle it has.
Blue bar = rotor disc. It tilts with the stick in both models. Nose is on the right, forward stick = nose down.
Mechanically, the cyclic tilts the rotor disc. A tilted disc produces a pitching moment, so the helicopter starts rotating and keeps rotating while the stick is held. That is model b. The pilot integrates in their head: push, wait, bring the stick back to stop the rotation at the attitude they want, then push the other way to return to level.
Model a only exists when something is doing that integration for the pilot:
If one of you pictures a raw mechanical cyclic and the other pictures a stabilised machine, you are both right and still talking past each other.