Hi

Both are government and top level engineering institutes of India.

IIT - Indian Institute of Technology

NIT- National institute of Technology 

NITs take admission through JEE Main rank and IITs take admission through JEE Advanced rank. There are total 31 NITs with approx. 18K seats and 23 IITs (Including ISM) with approx 10500 seats .

You can understand the difference between IITs and NITs from the below points
1- Quality of Education
When it comes to the quality of education provided IITs are ahead of the NITs. Both IITs and NITs are extremely good in providing education and producing good engineers, but at the same time the top IIT colleges have an edge because of their high standard of studies.
2- Production of young leaders and founders
The research conducted in the US proved that IITians are among the leading founders of the top startups in America. IITs are the only non US university with most number of founders of companies in the US.
Flipkart, a leading e-commerce was established by Sachin Bansal and Binny Bansal, who were IIT-Delhi pass outs. Arjun Malhotra is the co-founder of HCL Technologies and is an IIT-Kharagpur graduate. Simply 360 is a social media monitoring and analytics platform which was founded Bhupendra Khanal, who completed his studies from NIT-Durgapur. Microland technologies was started by Pradeep Kar, who completed his education from NIT-Nagpur.

All the best.