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1.
Polygyny is a form of Polygamy

Polygamy is the practice of a person, of either sex, having multiple spouses, at the same time.

Polygyny is the specific instance of a man being married to multiple women...
as opposed to Polyandry which is the specific instance of a woman being married to multiple men

LDS Mormons (prior to 1890) and FLDS Mormons (currently) are known for practicing Polygyny

RLDS Mormons have never practiced polygyny, or any form of Polygamy, in the history of their religion
John Thinks Polygyny is just fine, and so do all of his 4 wives
by DutchCappedCrusader June 29, 2014
 
2.
/noun/ -- the state in which a man is married to multiple wives. Mormon (RLDS)PolyGamy is exclusively of this type.
Ted has two wives, Jan and Ruth. PolyGyny is not legal in any of the states or territories of the US, but some adherents are said to live in Utah and Idaho.
by Ronald A.King November 19, 2005