The turn indicator has nothing directly to do with bank. The TC shows roll rate response as well as turn due to the gyro being mounted at 30 degs from the perpendicular. TheTC indication represents the sum of the roll rate and the yaw rate so it responds more quickly at the beginning and end of a turn than the TI.
The handicap of the TC is that it will show roll rate in turbulence and in this situation can be very difficult to follow.
Both instruments always have a slip ball as part of the display