Tri-cars were built to be a rental gun. From what I understand were a collaberation between Carter Machine and another company at developing a lower cost pump. I haven't seen many pop up in personal collections for sale by original owners but I have seen many come from old fields and I know of several that ran them.
They offer many pieces from the traditional Carter style to meet customers personal aesthetics while still offering a very durable pump that is user friendly and didn't have as high of tolerances. Basically I wouldn't let one of my friends who has never played before use my buzzard but I would certainly let them use a Tri-Car.
I would say the tolerances are still quite high as compared to other lower cost pump guns though.
Tri-Cars also share some of the same parts as other Carters of the time period, mainly the internals. I have found that the internals in my comp are almost exactly the same steel single screw bolt and hammer. I also think the powertube and valve retaining screw are very similar but the comps might have more porting.
This might not make sense to someone who hasn't handled an older comp (although it might still be the same today with newer comp but I don't have any dye or post dye) since the comp is undercocking and the tricar is side cocking.
The comps pump has a plate instead of a rod attached to the arm of the pump which is wide enough to house a set screw going through the center of it which screws into the bolt. This means that the bolt of the comp is threaded just like a single pump arm Tri-Car is.
The bolt on the tricar is also velocity adjustable and has an oring around the inside of it to keep it in place.
Hopefully that answers some of your questions DCB.
I personally wouldn't compare these to a phantom either, totally different feel.