Correct, accurate, exact, precise, nice, right are comparable when meaning conforming to standard, fact, or truth.
Correct, the most colorless term, implies scarcely more than freedom from fault or error, as judged by some (usually) conventional or acknowledged standard.
Accurate implies more positively fidelity to fact or truth attained by the exercise of care.
Exact emphasizes the strictness or rigor of the agreement, which neither exceeds nor falls short of the fact, a standard, or the truthc.
Precise stresses sharpness of definition or delimitation, or scrupulous exactness.
Nice implies great, occasionally excessive, precision and delicacy (as in discrimination, adjustment, or statement).
Right (see also GOOD) stresses an absence of deviation from and, therefore, a strict accordance with the facts, the truth, or a standard.
Often it is so close in meaning to correct that it is only in collocations where the latter’s stress on freedom from error or fault is set up against right’s emphasis on strict accordance with the facts, truth, or a standard that one can determine which word is preferable; thus, an answer to a problem in arithmetic may be said to be either correct or right; a gentleman of faultless manners and dress is said to be correct (not right); one seeking a friend in conformance with some socially or personally acceptable standard watches for the right (not correct) person.