Earlier quoted context omitted.
I always get scared when I accidentally have two shell sessions visible at once in tmux. I immediately exit one. I suppose I should read a bit on it. When I want side to side comparisons I go to the shell running emacs and do it there (post vague because I never remember the different words for windows and panes and shells etc these different apps use.)
tmux has a server containing sessions containing windows containing panes. Screen has sessions, windows, and panes (which it calls regions). I recently finally switched from screen to tmux and I found that it's pretty seamless (especially because I use vi keybinds in tmux still). Some machines at work don't have screen anymore.
Incidentally, this "screen absent" is why you should always volunteer to help create base shells (programmatically via packer not by hand) - emacs and tmux are always there when I made the image.