tmux, to me, feels like "modern screen". It has some cool features, but at the end of the day, it just wants to be a terminal multiplexer. Great!
Zellij on the other hand seems to offer terminal multiplexing as an obvious first-class use case but "not the whole point". At the surface, Zellij is an opinionated terminal multiplexer that uses a nice TUI to give discoverability which you can turn off when you're ready to gain screen real estate. It's easy to make Zellij behave exactly like tmux/screen, and it's easy to configure via a single config file.
Where Zellij takes a turn in to a different direction, however, is that the workspaces you can configure with it can do all sorts of interesting things. For instance I once built[0] a python cli app which had a command that would launch a zellij workspace with various tabs plugged in to other entrypoints of that same python cli, basically allowing me to develop a multi-pane TUI as a single python Typer app. In one pane I had the main ui, and then in another stacked pane I had some diagnostic info as well as a chat session with an llm that can do tool-calling back out to the python cli again to update the session's state.
I think wrapping up a project's dev environment as a combination of mise (mise.jdx.dev) and zellij or nix+zellij to quickly onboard devs to, say, a containerized development environment, seems like a really neat idea.
0: https://github.com/eblume/mole/blob/main/src/mole/zonein.py -- but this is mostly derelict code now, I've moved on and don't use zellij much currently.