Assuming for the sake of discussion that there was a proto-Sinaitic writing system that had symbols representing a word for "water" whose first phoneme was "m" and the symbol something waterish like this; and likewise something snake-like looking like this; then the transition to Phoenician it pretty simple, and the distance from Egyptian hieroglyphs is also less: in the Proto-Sinaitic "m" is basically the same as Egyptian "water", but with fewer zigs, and that's a reasonable simplification.
I would not say that Latin "M" and "N" look particularly different. It doesn't seem to be controversial that 𐌌 and 𐌍 were used in various old Italic writing systems and the modern letters M N some from these. The classical Etruscan version with these flipped with the long leg on the right seems to be a minority development, not characteristic of archaic Etruscan or Western Greek scripts. Basically the characters are the same, and what differs is whether you write left-to-right or right-to-left (start with the stick). The Latin and Etruscan characters are similar because they are really similar to Western Greek and the Greek looks like Phoenician (just ignore the flipping of letters as we move between languages). Phoenician 𐤌 and 𐤍 look like the Proto-Sinaitic symbols, which themselves look like Egyptian hieroglyphs.
Admittedly, linguists have mad skills at finding similarities where normal people see differences. My main caveat is that I distrust symbolically-reduced representations of ancient letters: I'd want to see actual photographs or tracings of the inscriptions.