What is the difference between `set -o emacs` vs `bindkey -e`?

From what I have seen, both set -o emacs and bindkey -e are used to modify the behavior of your terminal line editor to emulate emacs whereas set -o vi and bindkey -v are used to emulate vi keybindings. Since both set -o and bindkey seem to do the same thing, I was wondering what the differences between the two were and if there were any differences at all. It seems like set -o works for most shells whereas bindkey is a zle specific command. Is this the only difference? Also, do they bind the same keys or are there some keys where set -o and bindkey bind to different operations?