regress vs fall behind

regress is a noun but fall behind is not a noun.

Word	Noun	Adjective	Verb	Adverb
regress	Yes	No	Yes	No
fall behind	No	No	Yes	No

As verbs, fall behind is a hyponym of regress; that is, fall behind is a word with a more specific, narrower meaning than regress:

Other hyponyms of regress include drop off, fall back, recede.

regress (noun)	fall behind (noun)
returning to a former state
the reasoning involved when you assume the conclusion is true and reason backward to the evidence

regress (verb)	fall behind (verb)
go back to bad behavior	retreat
get worse or fall back to a previous condition	hang (back) or fall (behind) in movement, progress, development, etc.
go back to a previous state
go back to a statistical means