thirty-fourth vs 34th

thirty-fourth and 34th both are adjectives.

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

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

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

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