Which of these do you like, use, or want to try?
Email is pretty well-known; you can send a message to someone who is identified by "user" @ "website" (e.g. email@example.com ). A message contains a title, message, and an attachment; all fields are optional. Free email servers are often limited, and clients generally do not make it easy to "instant message", preferring messages to be substantial. An email message can be formatted with HTML but this is generally not desirable.
Forums can be emulated through the use of "listserv" mailing lists; PGP can be used for messaging signing (like a notarized signature) or message encryption.
Email clients are easily installed to multiple devices.
XMPP uses email style identifiers (e.g. firstname.lastname@example.org), but unlike email, has modern instant messaging features like online status (available, busy, away, offline) and status messages (eg "at work" or "on vacation"). XMPP servers are easy to find or setup, and most clients offer good encryption methods (especially via OMEMO). XMPP also supports multiuser chats, a primitive chatroom service.
An XMPP message will typically be 1-3 lines of text and lack markup formatting.
XMPP clients are easily installed to multiple devices.
IRC is primitive chatroom service. An IRC server allows users to either join chatrooms or private message users; some IRC servers allow account registration or incorporate something like voicemail. Generally speaking, you are only able to receive IRC messages while connected to a server; when you close your client, your user vanishes from the server, and messages during this period cannot be recovered. IRC users are identified by a "nickname" -- something like "test" or "some_user). They are generally short, pseudonymous, and can only be used by 1 client at a time.
IRC offers a very simple interface for writing chatbots, includes a limited markup format, and can allow for filesharing.
An IRC message will typically be 1 sentence or less.
IRC clients can only easily be used on 1 client at a time. Bouncers or remote servers can be used to remain online when you're done using your computer, or add your own 24/7 bots; it's more common for a user to have 1 user per device (eg johndoePhone, johndoeWork, etc).
Matrix is a very modern chatroom service that acts more like Discord than IRC; chatrooms / private messages/group chats, however, are often encrypted, and like IRC/XMPP/email, users and conversations are often spread across multiple servers. Some programmers and system adminstrators dislike it because the common server and client programs are resource-intensive, while users often dislike it because clients can be resource-intensive and the encryption logic is non-intuitive.
Attachments like URLs, video, images, etc are easily embedded in messages, and markup is easily used.
Matrix messages tend to be longer than XMPP or IRC messages.
Matrix clients can be used on multiple devices, with the caveat that the account owner must verify ownership of the devices to simply share encrypted messages between them.
I have no experience with this software, but I have heard that it's vaguely like XMPP built on top of the already existing email network. Encryption is allegedly simple.