Normally, yes! You'd be able to see threads across the Fediverse no matter where you signed up.

If you think of the Fediverse like a shopping mall, think of kbin and lemmy as two different bus companies that go to that same mall. It doesn't matter what bus you take, both take you to the same place where you can browse the same stores. Maybe you like the seats in the lemmy bus better than the kbin bus so you prefer to use that one. That's like if someone prefers the interface of lemmy more than kbin. While both go to the same places and see the same things, you might prefer the look and layout of one over the other so you use your favorite primarily.

However, keep in mind that kbin.social has had a massive amount of people sign up in the past few days, and as such it could not handle the large amount of new activity. They are working on a fix for this, but for now kbin.social has been cutoff from the Fediverse while it updates to handle the new load. Think of it like the kbin.social bus is not currently going to the mall -- you can get on, see and talk to the people on that bus, but until maintenance is done it won't actually go to the shopping mall where you can interact with everything across the Fediverse.

There is more to it but that's a simplified gist of it!

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.