So is the Mar Thoma Church and the Malankara Church the same?
No, they are different churches. There is another large group of Christians who are called "The Mar Thoma Syrian Church." This church has been influenced by the Anglican missionaries in India and is not in communion with the Oriental Orthodox Church. The name Malankara is a reference to the church of India in the same manner as the name Coptic refers to Egypt. Many Indian Christians today are known as "Malankara Orthodox" or "Syrian Orthodox."