put in vs cut in

put in and cut in both are verbs.

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

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

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

put in (verb)	cut in (verb)
place, fit, or thrust (something) into another thing	interrupt a dancing couple in order to take one of them as one's own partner
break into a conversation	mix in with cutting motions
to insert between other elements	break into a conversation
make an application as for a job or funding	drive in front of another vehicle leaving too little space for that vehicle to maneuver comfortably
set up for use	allow someone to have a share or profit
keep or lay aside for future use