partner vs significant other

partner and significant other both are nouns.

Word	Noun	Adjective	Verb	Adverb
partner	Yes	No	Yes	No
significant other	Yes	No	No	No

As nouns, significant other is a hypernym of partner; that is, significant other is a word with a broader meaning than partner:

partner: a person's partner in marriage
significant other: a person (not necessarily a spouse) with whom you cohabit and share a long-term sexual relationship

Other hypernyms of partner include domestic partner, spousal equivalent, spouse equivalent, relation, relative.

partner (noun)	significant other (noun)
an associate in an activity or endeavor or sphere of common interest	a person (not necessarily a spouse) with whom you cohabit and share a long-term sexual relationship
a person's partner in marriage
a person who is a member of a partnership

partner (verb)	significant other (verb)
provide with a partner
act as a partner