No in JoSAA Counselling, there are IIITs, NITs, GFTIs, IITs.
JEE Advanced score is only applicable to get admission into IIT. But to take admission into rest of the institutes.

Also you can check your Chances through our college predictor:

Hello,

If you have qualified for JEE Advanced 2024 or JEE Main 2024 and want to secure admission to the participating institutions (IITs, NITs, IIITs, and other GFTIs), then one has to register for JoSAA (Joint Seat Allocation Authority) counselling.

JoSAA is for not only JEE Advanced students but also for JEE Mains students.

Hope this helps,

Thank you