33rd vs thirty-third

33rd and thirty-third both are adjectives.

Word	Noun	Adjective	Verb	Adverb
33rd	No	Yes	No	No
thirty-third	No	Yes	No	No

As adjectives, 33rd and thirty-third are synonyms defined as:

33rd and thirty-third: the ordinal number of thirty-three in counting order

33rd (adjective)	thirty-third (adjective)
the ordinal number of thirty-three in counting order	the ordinal number of thirty-three in counting order