A chalazion is a non-infectious blockage of a meibomian gland on the eyelid resulting in an acute red, elevated nodule on the lid.
A hordeolum is an infected gland (Moll, Zeiss, Meibomian) on the eyelid resulting in an acute, painful nodule on the lid. An external hordeolum involves the Zeiss or Moll glands at the external edge of the eyelid.
An internal hordeolum is much rarer, but is an infection of the meibomian gland. Often times, the infection has spread beyond the glands into the surrounding tissues and if left untreated, could become a serious problem.