Mu.

Lemmy and mbin are different software. You are on lemmy.ca, which is a Lemmy instance. There are other websites that run Lemmy, notably lemmy.world, beehaw.org, and sopuli.xyz. They are different, independent websites, but they all run Lemmy, and thus are all Lemmy instances.

All these sites communicate with each other because Lemmy is based on ActivityPub, a protocol for letting social media accounts on different websites talk to each other. (A common analogy is that email lets people on different websites communicate because it’s all based on SMTP).

My account is on thebrainbin.org, a website that runs mbin. mbin is less popular than Lemmy, but there are still a few other websites that run it, including kbin.earth and fedia.io. Each of these sites is an mbin instance, and because mbin, like Lemmy, is built on ActivityPub, all those websites are able to talk to each other.

Now you might be thinking that, because Lemmy and mbin are both built on AcitivityPub, then logically accounts on Lemmy instances should be able to interact with accounts on mbin instances and vice versa. And if you think that, you are correct. The reason you see posts from Lemmy when using an mbin account and vice versa is that the various instances all use AcitivityPub to talk to each other, even though they’re on different websites.

But it doesn’t stop there! Mastodon is also built on ActivityPub, but aims to be like the website formerly known as Twitter, whereas Lemmy and mbin both try to be similar to Reddit. But because it’s all ActivityPub, accounts on Mastodon instances and interact with accounts on Lemmy and mbin instances and vice versa.

The same applies to other ActivityPub software, such as Sharkey (imitates Tumblr), Akkoma (also Tumblr), PeerTube (YouTube), and WriteFreely (blog).