I have a pet peeve regarding terminology when it comes to the "stringy thingy" used in Tenkara. I realize I am most likely speaking as a gang of one here.
A significant portion of Tenkaraists refer to the main portion of the "stringy thingy" as the leader, to which they attach the tippet.
The "stringy thingy" portion of the tenkara set up I personally like to use consists of three separate parts. A line (the furled gizmo), then a leader (which may be optional) then the tippet. Just like a western set up. I personally almost always use a tapered leader portion between my line (which is usually furled) and my tippet.
I've basically settled on two set ups -
When fishing still water for bass/bluegills, I usually am fishing a ponds from shore. For that situation, I've been using a 20' furled weight forward line, and a 6' two step tapered leader attached to a 4' final length of "tippet". I really like having the extra range, I can fish out to about 35'. Although I like fishing this longer set up, it may not be for everyone, it does require a bit more concentration when it comes to casting.
Probably 90% of my fishing is for trout, wading in large rivers, fishing mostly dries/damps. For trout fishing, I've been using a 10.5' furled triangle taper line, about a 7' two step leader ending up with a 4-5' length of tippet. That about all the line I usually fish even when using a western set up, so that suits my style of fishing just fine. It cast almost automatically, and allows me very good control for mending or animating my fly. If there is a down side, it does require a bit of hand over hand to get to the fish (as of course does the pond set up).
I realize that I am probably the one breaking with actual Tenkara tradition by including a leader. So it may just be my western mindset, but I would argue, er I mean discuss that in western fishing, the line is primarily used to provide mass which in turn is used to transmit energy applied by the angler via the rod. The leader provides a transition to the tippet. It seems like the "stringy thingy" that gets attached to the tenkara rod lilian certainly functions as a line, not as a leader. So it makes sense to me that when we refer to it in English, the terminology that should be used for the main section or the "stringy thingy" is line, not leader. (regardless whether or not an actual leader is included.