Is there such a thing as a sty, or is that just a name given to an ifected eye lid or tear duct?

Stye: A stye is an infected oil gland located where the eyelash meets the eyelid.

Blocked gland: Stye is the general term for a blocked, infected meibomian or oil gland. Everyone has scores of these glands on the edge of the upper and lower lids, and they usually produce the olily or lipid layer of the tears that prevents surface evaporation. When they become blocked with thickened secretions, they usually just stop producing, but can become infected and swollen. That becomes a stye.

Chalazion: The medical name for a stye is a chalazion. It's when an oil producing gland in the eyelid gets clogged and then irritated or infected. Depending on it's location and if it's infected it can also be called a hordeolum.

Definition of a sty: A "sty" is a common name for a new lump in the eyelid, just as a "cold" is a common name for viral pharyngitis. Hordeola are short term lumps with bacteria growing inside, often due to an infection in one of the oil glands in the edge of an eyelid. Chalazia are long term lumps filled with waxy material but are not usually infected. There can also be benign or malignant tumors of the eyelids.