Actually, the turn indicator is an instrument with a needle indicating the rate of turn but the important thing is that it responds only to yaw. There are certain modes of flight in which the turn co-ordinator, which responds to both yaw and roll, cannot be relied upon to give a correct reading and a turn indicator is essential.
It is not really correct to say that either turn indicator or co-ordinator respond to yaw. Their purpose is to indicate the rate of rotation about the normal axis i.e. how quickly you're turning (changing heading). While this can momentarily result from yawing, that's not it's primary purpose.
The difference in function between turn indicator and co-ordinator is a subtle one (there is a slight difference in how the gyro gimbal is arranged) but essentially the turn co-ordinator will respond to a limited extent to roll (a turn indicator will not). This means a turn co-ordinator will begin to show a turn as you roll into it, before your heading starts to change, making it more responsive.