Yes, these are both names for the same place. This place is also known as the Indo-Gangetic Plain.
This area covers most of the north and east of India as well as much of Pakistan and parts of Bangladesh.
To the north of this area are the Himalaya Mountains, which are the source of the rivers that have laid down the sediments that form the plains. The most important of these rivers are the Indus and the Ganges. The North Indian Plain is bounded on the south by the Great Plateau of Peninsular India.
The Great Plain of North India and North Indian Plain refer to the plains that lie between the Himalaya and the southern peninsula of Indian subcontinent. They stretch across northern India from east to west for about 2,410 kilometres, and have an average width of about 320 kilometres. The Northern Plains are formed by thee valleys of the rivers Brahmaputra, Ganges, and Indus rivers and their branches. This region makes up the world's largest plain formed of soil left by rivers. The soil of this plain ranks among the most fertile in the world.