Hii

The application form is single only, You are supposed to fill the application form once from the official NEET website and then appear in the NEET Exam.
If you qualify the required cutoff marks, you would become eligible for the councelling.
It is at this point when you need to fill two forms for the councellings. One would be registering for the All India Quota Councelling which will be conducted by MCC so you need to register yourself by filling the form on MCC official website.
Other is the state councelling for the state quota which will be conducted by the respectie state authorities. So you need to register for the particular state of that states particular website.
You can use following link for more details
https://medicine.careers360.com/articles/neet-counselling

Feel free to revert back for any more query.

Hope this help
Thankss!!