Dear Himu. 

 There is a difference...

The Ministry of Health and Family Welfare is responsible for all kinds of policies relating to health and family planning in India. The minister heading the ministry holds a cabinet rank.  Initially the Ministry had two departments  (i)  Department of Health and Family Welfare (ii) Department of Health Research. In August 2014, the Department of AIDS Control was merged with Department of Health & Family Welfare and is now known as National AIDS Control Organization (NACO).

The Medical Council of India (MCI) was a statutory body for establishing uniform and high standards of medical education in India. But recently the Supreme Court has dissolved MCI replacing it with a seven member board of governors led by NITI Aayog member health VK Paul.   The arrangement is a temporary one till the NMC (National Medical Council) Bill is passed by the parliament. 

JIPMER is an institute of National importance and is under the direct administrative control of Directorate General of Health Services (DGHS), Ministry of Health and Family Welfare, Govt of India.

Hope this helps