tonsillectomy vs cutting out

tonsillectomy and cutting out both are nouns.

Word	Noun	Adjective	Verb	Adverb
tonsillectomy	Yes	No	No	No
cutting out	Yes	No	No	No

As nouns, cutting out is a hypernym of tonsillectomy; that is, cutting out is a word with a broader meaning than tonsillectomy:

tonsillectomy: surgical removal of the palatine tonsils; commonly performed along with adenoidectomy
cutting out: surgical removal of a body part or tissue

Other hypernyms of tonsillectomy include ablation, excision, extirpation.

tonsillectomy (noun)	cutting out (noun)
surgical removal of the palatine tonsils; commonly performed along with adenoidectomy	surgical removal of a body part or tissue