If we're going to be pedantic, the em is a unit of width that depends on the font, but not necessarily the with off an m. Some texts apparently used to define it as the width of the capital M, but this definition is obsolete. source

So that’s where the name comes from. I never would’ve guessed it was something this straightforward :)

On that note, are em dashes and en dashes identical in monospace fonts, if every letter is the same width?

Edit: I tested this on a few monospace fonts, and they have a character for en dashes but not em dashes