I don't have zsh setup on the OS I'm running currently, but a simple example is that the light-grey autocomplete text from zsh/oh-my-zsh shows up on i3-tmux but not tmux (at least at the time of writing).

I honestly don't remember the exact details, and maybe it's now fixed.

Most likely you are using the wrong TERM so tmux doesn't have the correct information about what colours your terminal supports.