When looking through my badges, I noticed that some badges have a silver background while most have a black background. This occurs for both bronze and silver badges. All of my gold badges have the black background. What does the different background color mean, if anything?
Silver badges are Tag badges
As can be seen on the Badges page.
All other badges come up as black.
The reason you have no gold badges that are silver is because you haven't answered enough questions in one tag to get it. Your two closest are marvel and star-wars which are 117 and 135 questions off, and 307 and 210 up-votes off, respectively