housebreaking vs breaking and entering

housebreaking and breaking and entering both are nouns.

Word	Noun	Adjective	Verb	Adverb
housebreaking	Yes	No	No	No
breaking and entering	Yes	No	No	No

As nouns, housebreaking and breaking and entering are synonyms defined as:

housebreaking and breaking and entering: trespassing for an unlawful purpose; illegal entrance into premises with criminal intent

Other synonyms of housebreaking include break-in.

housebreaking (noun)	breaking and entering (noun)
trespassing for an unlawful purpose; illegal entrance into premises with criminal intent	trespassing for an unlawful purpose; illegal entrance into premises with criminal intent