Are BHU and IIT BHU the same institute ?

No, BHU and IIT BHU are not the same institutes. Previously IIT BHU used to be a part of BHU and even after it became IIT, it still shares the same campus but IIT BHU is an autonomous institute. To go into detail, BHU stands for the Banaras Hindu University. Clearly, as the name suggests it's a University that comprises 6 institutes, 14 faculties(streams), and 140 departments. It has over 75 hostels for the resident students. The well-known institutes include Indian Institute of Technology(IIT BHU), Institute of Medical Sciences(IMS BHU), Institute of Agricultural Sciences(IAS BHU), Institute of Science(I.Sc. BHU), Institute of Management Studies(IMSt.-BHU) and Institute of Environmental and Sustainable Development(IESD BHU). The faculties are as diverse as Faculty of Law(FL-BHU), Faculty of Arts(FA-BHU), Faculty of Performing Arts(FPA-BHU) and Faculty of Commerce, etc. The departments are really diverse as well; the Department of Journalism, Department of Linguistics, Department of Mass Communication to name a few. It is a well-known fact that there is no other university in the country that offers as many courses as the Banaras Hindu University does.

On the other hand, IIT BHU is the Engineering institute. It was formerly known as IT(Institute of Technology) BHU. It was designated the tag of an IIT in the year of 2012. The admission to IIT BHU is based on the JEE(Advanced). The institute has 11 Engineering departments, 3 dedicated Science departments, 3 Schools and a Humanities department. It offers courses across undergraduate and postgraduate streams. IIT(BHU) is known for offering very diverse UG and PG programs. For example, it is the only premier institute in the country to offer courses in Ceramics Engineering.