Hello Aspirant ,

There is not much of a difference, between them, a deemed university is a status of independence given by the  Department of Higher Education (DHE), MHRD, on the advice of UGC, they are neither private nor government. This means that they will have full autonomy in deciding what courses to offer  , their curriculum ,admission procedure ,the fee structure etc. Basically they can make their own rules regarding anything,they are all on their own. On the other hand private universities are independent too but they still have to follow UGC's rules and regulation to function,as they are approved by them . The deemed universities are authorized to give their own degree/diploma.So basically the difference is that deemed universities are more flexible compared to private universities . The fee structure is almost the same in both and  will vary with different courses from college to college but always it is way more than a state or central university. Regarding the admission , if it is medical it based on NEET exam for all types of colleges and after clearing the exam you can attend the all India or state counselling.The Medical counselling committee will conduct counselling for the 15% from AIQ , and 100% seats of Deemed and Central universities.The designated state counselling authorities will grant seats based on NEET score for the rest of 85% of government colleges and all the private colleges.

All the best

Hope it helps