MLA in India stands for Members of Legislative Assembly. They are elected by the people. They then become members of the legislative assembly and also form the government. 

MP in India stands for Members of Parliament. They are known as directly and indirectly elected representatives of the country in the union government. Both the members of Lok Sabha and Rajya Sabha are called MPs or Members of Parliament.

Further Reading:

• State Legislature – Article 168 – 212
• Parliamentary Committees 
• Functions of the Parliament