engage vs hire

engage

verb
  • To arrange to employ or use (a worker, a space, etc.). 

  • To enter into conflict with (an enemy). 

  • To come into gear with. 

  • To enter into (an activity), to participate (construed with in). 

  • To draw into conversation. 

  • To mesh or interlock (of machinery, especially a clutch). 

  • To attract, to please; (archaic) to fascinate or win over (someone). 

  • To guarantee or promise (to do something). 

  • To engross or hold the attention of; to keep busy or occupied. 

  • To bind through legal or moral obligation (to do something, especially to marry) (usually in passive). 

  • To enter into battle. 

hire

verb
  • To employ; to obtain the services of (a person) in exchange for remuneration; to give someone a job. 

  • To occupy premises in exchange for rent. 

  • To accept employment. 

  • To obtain the services of in return for fixed payment. 

  • To accomplish by paying for services. 

  • To exchange the services of for remuneration. 

  • (neologism) (in the Jobs-to-be-Done Theory) To buy something in order for it to perform a function, to do a job 

noun
  • Payment for the temporary use of something. 

  • A person who has been hired, especially in a cohort. 

  • The state of being hired, or having a job; employment. 

How often have the words engage and hire occurred in a corpus of books? (source: Google Ngram Viewer )