Selection guidelines from Coilcraft. Link here (PDF)
Current sensors detect the flow of AC or DC current in a wire or circuit trace. They can be used to detect an on/off/ pulse current condition or to measure the magnitude of the current in the wire or trace. This discussion is limited to AC current sensors. Ideal current sensors would not use any power to detect the current in the wire or trace, but real current sensors require some of the circuit energy to provide the information.
Current sensors are frequently used to measure and control the load current in power supplies, safety circuits and a variety of control circuits. In applications where controlling the current is required, such as in power supplies, accurately sensing the magnitude of the current is a fundamental requirement.
In pulsed-current applications or where it is only required to detect an on condition such as some safety circuits, the precise magnitude of the current may not be required. In other safety circuits, the sensed current can be used to trigger a shut down when the current exceeds a pre-set limit.