Ok, just to clarify, my original struggle was to understand what made tmux different from using some terminal app and just split the screen xD

Not every terminal emulator has window splitting capabilities. Some, like Alacritty, specifically expect you to run a program like tmux if you want this functionality. Splitting within tmux also makes it vastly easier to multitask on a remote host via SSH: if you run a remote tmux, every split window is already running on the same remote host, no need to log in again and again.