Bright Garden, to your #32 (or was it #33?) - The handle at top right in the post #30 photo of several handles looks like a mono-line handle.
The long 'wire' with the bobbin in the middle is actually two solid wires twisted together along their length. The bobbin has a slot just wide enough to fit the wire diameter, and just long enough to fit the pair of them. At the handle end, the wires run in a bearing that can withstand the model's pull, yet let the bobbin rotate the twinned solid wires..
As mentioned above, the end of the flying line is formed to loop like the eye of an oversize knitting needle. The AMA Rulebook has good illustrations of how to make and use this kind of connection. Visitors to the AMA website can have access without joining as members. (I consider membership worthwhile. A personal thing...) A split bead or very small bobbin connects that wire to the controller.
Remember - you hold the bobbin from rotating, and slide it towards you or away to make it rotate the twisted wire pair to put turns into the flying wire. THAT'S what turns the 'cam' unit at the model. (As mentioned, consecutive loops have the same effect as sliding the controller bobbin. You can let go of it to spin it along the twist to restore neutral where you want it.)
Mono-line is most useful for speed models. The 1/2A model with the metal pan looks like it is for the "Proto Speed" event. Nice decorations on the decoration, no?
The black handle is the traditional U-Reely. It and the smaller ones in the middle require your lines to be closely matched in length. Adjustment for a comfortable neutral is limited. The yellow handle with a flat metal plate does allow some adjustment.
The large handle on the right is a 3-line unit that can operate a throttle. The "science" of that is fascinating! The trigger and the lever out the top are connected, and operate the other function. The top and bottom lines are for 'elevator' control. unless you really need a throttled CL model, fussing with 3-lines is a nuisance. The standard 2-line setup is much more natural feeling, and easier to hook up.