Blog/Featured Posts are the same

Hello. I have set up my Homepage/Frontpage Settings > Display category. It displays category on home page just fine. I added a blog and set parameters as Settings > Reading > Changed to A Static Page | Front page: -Select- | Posts Page: Blog When I click on my blog page, it will only show the posts I checked off under Homepage/Frontpage > Display. I tested by highlighting 2 categories and the same thing happened. The posts in the 2 categories showed up on home page and blog page. Is there a way to have posts from certain categories on home page and all posts appear on blog page. Thanks.