What is the difference?
Eddy currents are one case of electromagnetic induction, usually an undesired one. In this case, a varying magnetic field causes current loops in the bulk of the conductor. For example, some transformers have two coils of wire around a common iron core. When we apply AC current to one coil, there is an induced potential across the second coil that can generate induced currents if the ends of the coil are shorted or hooked up to a load. This is the desired operation of the transformer. However, at the same time, there are current loops being induced in the bulk of the iron core and we would call those eddy currents. The eddy currents are undesirable because those currents will be dissipated into heat, wasting that power instead of allowing the first coil to efficiently transfer power to the second coil. This is why transformer cores are laminated (i.e. made of sheets glued into a stack with non-conducting glue) to prevent large, power guzzling eddy from forming. See the wikipedia article on transformers.
The comment by @Floris brought to mind an extreme case of eddy current damage. Search for "coin shrinking", for example see the video here. The eddy current actually distorts the metal.
Eddy currents are induced circular currents in conductors exposed to an AC magnetic field. The term is often used for induced currents that cause unwanted heating and losses in conductors, e.g. in transformers and electrical machines. On the other hand, they are also being put to good use in eddy current brakes and inductive heating.