The definition of unique is one of a kind.
Distinct among others of a kind:
That has no parallel, equal, or counterpart; unmatched
Having no precedent or parallel; unheard-of; novel
The definition of rare is something that exists in limited quantities, that is unusually good, or meat that is not cooked until it is well done.
Serving to identify; distinguishing or characteristic:
Showing a marked departure from previous practice; new:
Find another word for one-of-a-kind. In this page you can discover 10 synonyms, antonyms, idiomatic expressions, and related words for one-of-a-kind, like: unique, in a class by itself, special, unparalleled, unprecedented, rare, distinctive, original, covetable and null.