Technically they are of course different, but on concept they are alike: both are decentralized, where server form the network and where the user has an account at such a server. The server (temporarily) stores the messages and metadata. This means the user normally has to trust the server, as it stores the user's data. However, in both cases you can run your own server, and/or use extra end-to-end encryption.

I think e-mail with IMAP IDLE is still ahead over lot of the more ""modern"" messaging systems: both my Jolla and my desktop notify me of a new e-mail as soon as it arrives. Now it doesn't matter on which client I open that e-mail, the other clients immediately know I've opened it and dismiss their notification. They share a common state.

With xmpp, on the other hand, I only get the message at one client, the one with highest priority configured. It sucks when messages arriving on only on my phone, which lays in the next room, even though I'm sitting behind my desktop. There are extensions to remedy this (message carbons, chat log storing and retrieval from the server) but well, as said, clients are still lacking

At least xmpp allows you to login with multiple clients at the same time. Tox doesn't seem to support that.