Kind of, but there is one more layer.

ActivityPub allows more than one type of data (or rather it's all just data, it's the medium in which the user uses it?). MSTDN.ca, Lemmy.ca, lemmy.world, et al are the equivalents of an email server. Lemmy, kbin, Mastodon are different services running on the ActivityPub backbone. There is a fair amount of cross-compatibility, since they are all using ActivityPub. You can easily subscribe to a Lemmy community with your Mastodon account, or a kbin magazine with your Lemmy account. It just might be a little messy.

Remember when Microsoft started pushing "rich" email? If you were using a text based email client, you'd get all the HTML formatting tags. It was still email, you could still read it, it was just messy. Likewise, my experience with Lemmy via Mastodon was that you loose the threading and grouping. Comments tended to show as random messages out of context. Absolutely works, just less nice than using Lemmy for Lemmy and Mastodon for Mastodon. I will say that kbin magazines seem fine on Lemmy, but I haven't really played with kbin yet, so I may not know what I'm missing.

So the email analogy has it's limits. BeeHaw.org, Lemmy.ca, sh.itjust.works are like email servers that all focus on one format of email. MSTDN.ca, mastodon.social, mas.to, Universeodon.com, etc. are also all email servers focusing on a different format for email. They can all talk to each other, but emails from the wrong format won't fit in as well.

I think your question and my answer strain the limits of using an an analogy to simplify a concept. Might be almost ready to abandon analogy and just directly learn about Federation.