Just to clarify a previous response:
Both Moving Magent (MM) and Moving Coil (MC) cartridges rely on the fact that a wire moving in a magnetic field generates an electrical signal.
In a MM cartridge, the coils (one per channel) are fixed. and a permanent magnet attached to the stylus provides the varying magnetic field as it vibrates in response to the record grooves. The MM cartidge benefits include relative ease of manufacture, ruggedness, high output, and user-replacable stylus.
A MC cartidge reverses the mechanical positions of the magenet and the coils. The permanent magnet is fixed, and the coil is attached to the stylus. The coil vibrates in response to the record grooves, thus generating a signal.
This coil has much lower mass than the permanent magnet attached to the stylus of MM cartridge, so the MC cartridge has better transient response than the MM cartridge, and often have a better high end. This comes at a cost - the low mass moving coil contains much less wire than the fixed coils of the MM cartridge, so the MC cartridge has very low output and low impedance, thus requiring a step up transformer and/or special phono preamp.
The MC stylus is not user replaceable. Stylus replacement involves a cartridge rebuild.
There is a third type of magnetic cartridge called a Moving Iron (MI) cartridge. This uses a fixed permanent magnet and fixed coils. A low mass piece of iron (or other magnetic material) sits between the coils and the permanent magnet, and is attached to the stylus. As the stylus vibrates, the attached piece of iron modulates the magnetic field from the permanent magnet. This varying magnetic field generates an electrical signal in the coils.
MI cartridges have all the advanages of the MM cartridge, and have some of the transparency and transient response associated with MC cartridges, since the piece of iron is much lighter than the permanent magnet in the MM design.
The Grado product line consists of MI cartridges