day-after-day vs day-by-day

day-after-day and day-by-day both are adjectives.

Word	Noun	Adjective	Verb	Adverb
day-after-day	No	Yes	No	No
day-by-day	No	Yes	No	No

As adjectives, day-after-day and day-by-day are synonyms defined as:

Other synonyms of day-after-day include daily, day-to-day.

day-after-day (adjective)	day-by-day (adjective)
of or belonging to or occurring every day	of or belonging to or occurring every day