All moving tailplane
A search on google using 'stabilators on aircraft' comes up with masses of info. As usual wikipedia has a concise explanation. I was tempted to put my email address in my profile so you could email me. A long shot but did you fly at the pointed end of BA/BY? and did you once suffer an erroneous fire warning in a JP?
Interestingly the feel in PA28/PA34 is maintained by an anti - servo tab which also acts as a trim tab. Some think anti -(over?) balance tab would be a more appropriate name as it helps to stop the CP (AC) moving across the hinge line and giving you more movement of the stabilator than you demanded.
I will now see if you have an email address on your profile.