Assuming that you are referring to seats at medical college for admission through NEET, I assume that you want to know the difference between a private quota seat and a private seat.

Mainly, admission through NEET in Karnataka is either through 15% All India Quota or 85% State quota. This state quota is also referred to as state 'government quota' seats, which includes seats in government medical colleges as well as private medical colleges. I believe that a private seat here refers to a seat in a private medical college under state government quota, for which you have to pay less fees. You need to score good marks in NEET to get such seats.

The other private quota seat you are referring to here is I believe the private/management/NRI quota seats available at private medical colleges in Karnataka. If you haven't scored well in NEET but got the qualifying marks, you can opt for these seats, which will cost about 7-8 lakhs per year.

Hope I have answered your question.