The Patron banners are for people who have donated to the site. After you've donated I think you PM Jason and he hooks you up with one. Or maybe the Patron system is over, since it was for a pretty specific donation drive.

The Zelda Wiki Contributer banner is for pretty much exactly what it says. People who have made significant contributions to the Zelda Wiki.

All this and more info can be found in the Newbies Guide.