As a separate question, I'm also trying to understand the difference between a turn indicator and a turn coordinator.
I think the turn indicator was an instrument with a needle indicating the rate of turn (not the "wings"). It might not have been equipped with a ball (slip indicator is the correct name?). I would say the turn coordinator has always to be equipped with a ball since in order to achieve a coordinated turn the ball must be in the middle (no slip/skid).
In theory you don't have to keep the angle of bank (as opposed to rate of turn which should be kept) constant and achieve a coordinate turn (speed change is required), the ball should always be middle (ish).
I see why these two instruments are a bit confusing, in normal controlled flight their indications might be similar, maybe you can ask an instructor to demonstrate a fully developed spin (in an approved aircraft) and observe the instruments (a lot of braveness required!) - this is the point where the direction of turn is most important (and correctly always shown only on turn indicator/coordinator) in order to regain controlled flight. Maybe the instructor could also demonstrate some less drastic ways of opposite indication for these 2 instruments - some suggested here previously.