EMC: Electromagnetic Compatibility means that equipments or systems can be operated in electromagnetic environment, and don't produce electromagnetic interference to other equipments in the environment. Therefore, EMC inlcudes two sides requirements: first, electromagnetic produced by equipments during normal operation can't  exceed related limitation; second, equipments has immunity to existing electromagnetic in the invironment, as know as electromagnetic sensitivity.
EMI: RE, CE, Harmonic, Flicker
EMS: ESD, EFT, DIP, CS, RS, Surge, PFM