EMC testing vs. EMI testing
Electromagnetic Interference is a radiated or conducted signal that is unwanted that you are trying to avoid.

Electromagnetic Compatibility encompasses the standards and testing of equipment so that it can generally be expected to function properly in a shared environment. This involves testing devices to make sure that the EMI produced is under some limit, and testing to ensure that the susceptibility is above some threshold where most complying devices won't disturb it (or damage it, depending on the standard).

Additionally EMC susceptibility testing can check for immunity to environmental factors such as static discharge (ESD) and line transients that can occur in normal use.