twenty-third vs 23rd

twenty-third and 23rd both are adjectives.

Word	Noun	Adjective	Verb	Adverb
twenty-third	No	Yes	No	No
23rd	No	Yes	No	No

As adjectives, twenty-third and 23rd are synonyms defined as:

twenty-third (adjective)	23rd (adjective)
coming next after the twenty-second in position	coming next after the twenty-second in position