If you have a national park pass will you have to get a discovery pass to camp in a state park?

A national park pass will not work for this Washington State park

You will need a discovery pass according to the sign at the entrance

National pass does not get you into a state park. Also for canping you do not need a discovery pass. If you are visiting for the day then you need a day pass or a discovery pass both of which you can buy at the park.

If you are paying for a campsite, your parking will be covered. Otherwise you need a day pass

No - you will have to purchase either a day pass for 10$ for that park only or a 30$ Discover pass for all Washington State Parks that is good for 1 year

A Discovery Pass is required at Washington State parks. I don't believe a daily pass will allow an overnight stay. Both can be purchased at the entrance to the park. A National Park pass will not allow admission or parking.

Far as I know yes