third party vs arbiter

third party and arbiter both are nouns.

Word	Noun	Adjective	Verb	Adverb
third party	Yes	No	No	No
arbiter	Yes	No	No	No

As nouns, arbiter is a hypernym of third party; that is, arbiter is a word with a broader meaning than third party:

third party: someone other than the principals who are involved in a transaction
arbiter: someone chosen to judge and decide a disputed issue

Other hypernyms of third party include arbitrator, umpire.

third party (noun)	arbiter (noun)
a political party organized in opposition to the major parties in a two-party system	someone chosen to judge and decide a disputed issue
someone other than the principals who are involved in a transaction	someone with the power to settle matters at will