loosen up vs disengage

loosen up and disengage both are verbs.

Word	Noun	Adjective	Verb	Adverb
loosen up	No	No	Yes	No
disengage	No	No	Yes	No

As verbs, disengage is a hypernym of loosen up; that is, disengage is a word with a broader meaning than loosen up:

Other hypernyms of loosen up include free.

loosen up (verb)	disengage (verb)
become less tense, rest, or take one's ease	become free
cause to feel relaxed	release from something that holds fast, connects, or entangles
make one's body limber or suppler by stretching, as if to prepare for strenuous physical activity	free or remove obstruction from
cause to become unblocked
become less tense, less formal, or less restrained, and assume a friendlier manner