confession vs admission

confession and admission both are nouns.

Word	Noun	Adjective	Verb	Adverb
confession	Yes	No	No	No
admission	Yes	No	No	No

As nouns, admission is a hypernym of confession; that is, admission is a word with a broader meaning than confession:

confession (noun)	admission (noun)
(Roman Catholic Church) the act of a penitent disclosing his sinfulness before a priest in the sacrament of penance in the hope of absolution	the act of admitting someone to enter
an admission of misdeeds or faults	the right to enter
a written document acknowledging an offense and signed by the guilty party	an acknowledgment of the truth of something
a public declaration of your faith	the fee charged for admission
the document that spells out the belief system of a given church (especially the Reformation churches of the 16th century)