The handlebar setup also changes the way a seat feels. but a seat should be comfortable.
You will feel the seat press on your bones, but it should not hurt. Soft seats don't support the spine and hips like a firmer seat. It's important not to have something too wide or narrow. You can actually get fitted for a seat now and they'l measure your sit bones. It's worth doing, but even if the measurement is technically right it is still subjective.
A more padded seat should still be firm enough, if it's too soft your basically squashing everything fleshly and bone into the seat, after a little pedal it hurts.
I got measured recently and my new seat is much better, the pain was reduced greatly. Getting measured will help, you can be slightly wider, but if you are too narrow the body isn't supported and the pain is increased.
Find a good bike shop or sporting good store that has demo seats to try, they can measure you or you can just try different ones. It's not worth spending a lot of money if the seat doesn't fit.