butt in vs cut in

butt in and cut in both are verbs.

Word	Noun	Adjective	Verb	Adverb
butt in	No	No	Yes	No
cut in	No	No	Yes	No

As verbs, butt in and cut in are synonyms defined as:

Other synonyms of butt in include barge in, break in, chime in, chisel in, put in.

butt in (verb)	cut in (verb)
break into a conversation	interrupt a dancing couple in order to take one of them as one's own partner
	mix in with cutting motions
	break into a conversation
	drive in front of another vehicle leaving too little space for that vehicle to maneuver comfortably
	allow someone to have a share or profit