Mattermost

Mattermost is an open-source, self-hostable online live chat service with file sharing, search, and integrations. It is designed as an internal chat for organisations and companies, and mostly markets itself as an open-source alternative to Slack.com[9][10] and Microsoft Teams. https://en.wikipedia.org/wiki/Mattermost

Deployment: Mattermost offers more control with self-hosted and private cloud options, while Matrix.org's decentralized nature allows for a federated network of servers.
Integration: Mattermost has a strong focus on integrating with developer tools, enhancing technical workflows, whereas Matrix emphasizes interoperability between different communication platforms. https://www.restack.io/docs/mattermost-knowledge-mattermost-vs-matrix-comparison

Mattеrmost focuses on ChatOps tools and catеrs to thе dеvеlopеr community, offеring sеamlеss communication intеgration into workflows. On the other hand, Elеmеnt is prеfеrrеd by small businеssеs that provide tailorеd solutions with usеr friеndly intеrfacеs. Emphasizing vеrsatility, Elеmеnt facilitatеs strеamlinеd communication in smallеr tеams. https://www.rocket.chat/blog/mattermost-vs-element