Promise, engage, pledge, plight, covenant, contract are comparable when they mean to give one’s word that one will act in a specified way (as by doing, making, giving, or accepting) in respect to something stipulated.
Promise implies a giving assurance either orally or in writing but it suggests no further grounds for expectation of the fulfillment of what is promised.
Engage implies a more binding agreement or more definite commitment than promise. Typically it is used in formal or consequential situations, sometimes specifically implying an agreement to marry and sometimes an agreement to accept as an employee. It ordinarily implies a promise regarded as binding and to be relied on and especially one concerning conduct over a period of time.
Pledge (compare PLEDGE ), aside from uses in connection with drives and charities, may imply the giving of a promise by some act or words that suggest the giving of a solemn assurance or the provision of a formal guarantee.
Plight implies a solemn promising and persists chiefly in a few stereotyped phrases such as “plight one’s troth.”
Covenant implies at least two parties to the promise, each making a solemn agreement with the other.