Why can I make an alias beginning with `:` colon, but not `;` in zsh?

; is a special shell character used to separate commands; for example this:

% ls /; ls /etc

Is (mostly) the same as if you had typed:

% ls /
% ls /etc

A : on the other hand is merely a special shell builtin, and can be overridden.

There may be tricks to override this; you can't "just" override it with functions either, but I would strongly recommend against it as I suspect it will only bring you confusion and errors. There are plenty of other characters on the keyboard that can be used :-)

That said, you can use a global alias to override ; to call a function:

% alias -g ';'='semicolon'

% semicolon() { print -r -- semicolon: $@ }
% ;hello
semicolon: hello

You'll have to modify that semicolon function though.

Note this will apply everywhere on the commandline, including in the middle of a command:

% ls ; ls 
ls: cannot access 'semicolon': No such file or directory
ls: cannot access 'ls': No such file or directory

You could modify the semicolon() function a bit to be smart about at least some scenarios, but I would strongly recommend against it.