Inhauler, twing, tweak, barber hauler. What is the correct term. I always thought it was barber hauler.
Les, I use the term inhauler as a general term for what it does and, here, to stay with the terminology used by the OP. There is a difference between a Barber hauler and a twing.
I've only recently learned what a twing is, but a Barber hauler is usually an out hauler because it was originally connected to a block on the toerail or a stanchion post base to open the slot. The term, I think is used for inhaulers, as well and they traditionally attach directly to the jenny clew.
A twing, as best I can find, are down haulers that use a ring or 'beaner on the jib sheet. They are often combined with an inhauler. This is mostly new to me, but consistent with the little I already knew about Barber haulers. Here's an illustration of a twing.
Oddly, most of the examples I've found of twings have them attached at the head of the traveler track. I don't know why the traveler car can't do exactly the same function in that case.
-Will (Dragonfly)