34th vs thirty-fourth

34th and thirty-fourth both are adjectives.

Word	Noun	Adjective	Verb	Adverb
34th	No	Yes	No	No
thirty-fourth	No	Yes	No	No

As adjectives, 34th and thirty-fourth are synonyms defined as:

34th and thirty-fourth: the ordinal number of thirty-four in counting order

34th (adjective)	thirty-fourth (adjective)
the ordinal number of thirty-four in counting order	the ordinal number of thirty-four in counting order