Universities, banks, and hospitals are all institutions. Until you arrived at the bank, you'd forgotten that financial institutions were closed for the holiday. Thank goodness for the ATM! The noun institution also refers to a long held custom or practice in society. Even if your parents divorced when you were young, you might strongly believe in the institution of marriage. Or you might believe that once you enter the institution of marriage, your next stop will probably be a mental institution.
A consultant (from Latin: consultare to deliberate) is a professional who provides expert advice in a particular area such as security (electronic or physical), management, education, accountancy, law, human resources, marketing (and public relations), finance, engineering, science or any of many other specialized fields.
A consultant is engaged to fulfill a brief in terms of helping to find solutions to specific issues but the ways in which that is to be done generally falls to the consultant to decide, within constraints such as budget and resources agreed with the client.