kbin.social and fedia.io are two separate websites. They are called "instances". Collectively, these sorts of sites are referred to as the "fediverse".

Posts on one "fediverse" site can be see on another "fediverse" site. For instance, right now you're apparently posting from beehaw.org, which isn't a kbin instance but instead appears to be a lemmy instance.

I'm currently using fedia.io, which is a kbin instance.

The group we're in right now is technology@beehaw.org, which is hosted on the beehaw.org website/instance, which is the site you're using right now. But I can see and interact, since we're together on the "fediverse".

If you signed up for kbin, you have a kbin username as well, but it's separate from your beehaw account. For example, I'm @Otome-Chan@kbin.social but also @April, I don't have a beehaw account so any posts I make on beehaw groups will have to be from either my kbin account or my fedia account. whereas you can respond with your beehaw account as you've done here :)

So yes, it's the same "fediverse" between kbin, fedia, and beehaw. Though notably kbin.social is having some issues with federation right now due to lots of people joining it.