Matrix is a communication protocol, such as IMAP+SMTP communication protocols that are behind emails. This means that the "communication stack" when you use Matrix, as well as when you use emails, can be summarized in 3 parts:

• the client (the app you use to chat, such as Apple Mail or Outlook for emails, Element or FluffyChat for Matrix)
• the provider (who is offering you the service, such as gmail.com or yahoo.com for email, matrix.org or chat.mozilla.com for Matrix)
• the server (the app that your provider runs to let you chat, for emails all most famous providers have their own proprietary servers, for Matrix the two main options for server are Synapse or Dendrite)

I haven't read the article properly yet, but from what I've understand for now it seems Commune.sh aims to build a new client for Matrix that reproduces the layout and features of Discord, while at the same time being based on an open communication protocol and therefore having all its related benefits.

Seems pretty promising, I'm gonna keep an eye of it 👀

Discord and matric are room based chat services. You join a room and there's a chat around some subject going on which you can participate in. I use it for my DND group to discuss upcoming games and our general lives. Some larger communities form on these apps. Say, game emulation, people who talk about a video game, college members and alumni, people in a city, weed in a country, youtubers, etc.

This seems to be a bridge that copies messages from discord and sends them to matrix, or copies messages from matrix and sends them to discord. Allowing users from one service to talk to the other. The intent is to slowly bring members of a larger discord community over to the matrix server.