different between membership vs familiarity

English

From member +? -ship.

membership (countable and uncountable, plural memberships)

The state of being a member of a group or organization.
The terms of membership agreement were vague.
He has memberships in clubs in three cities.
The body of members of an organization.
The memberships of the state chapters elect delegates to the national convention.
(mathematics) The fact of being a member of a set.

From Middle French familiarité, from Latin famili?rit?tem. Displaced native Old English h?wc?þnes.

Morphologically familiar +? -ity

familiarity (countable and uncountable, plural familiarities)

The state of being extremely friendly; intimacy.
- 1677, Hannah Woolley, The Compleat Servant-Maid, London: T. Passinger, p. 2,^[1]
  Do not keep familiarity with any but those, with whom you may improve your time.
Undue intimacy; inappropriate informality, impertinence.
An instance of familiar behaviour.
Close or habitual acquaintance with someone or something; understanding or recognition acquired from experience.

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