tyrannize vs push around

tyrannize and push around both are verbs.

Word	Noun	Adjective	Verb	Adverb
tyrannize	No	No	Yes	No
push around	No	No	Yes	No

As verbs, push around is a hypernym of tyrannize; that is, push around is a word with a broader meaning than tyrannize:

tyrannize: rule or exercise power over (somebody) in a cruel and autocratic manner
push around: be bossy towards

Other hypernyms of tyrannize include ballyrag, boss around, browbeat, bully, bullyrag, hector, strong-arm.

tyrannize (verb)	push around (verb)
rule or exercise power over (somebody) in a cruel and autocratic manner	be bossy towards
rule a country as a tyrant