Why are some Emacs functions not available via `M-

This Stack Overflow answer told me that I can set Emacs’s font size with set-face-attribute:

(set-face-attribute 'default nil :height 100)

The comments reveal that you can’t run set-face-attribute with M-x:

Instead, you have to run it with M-::

Why are some commands, like set-face-attribute, not available via M-x?

M-x is bound to the command execute-extended-command, which lets you type the name of a command and runs it.
M-: is bound to the command eval-expression, which lets you type an arbitrary S-expression containing function calls and evaluates it.

Functions, which you can call with M-:, are used to implement Emacs features, customizations (such as in your .emacs), and plugins. Function arguments are normally passed by calling the function in an S-expression.

Any function can also be a command if it has an interactive form in its definition. The interactive form describes how the function should get its arguments when called as a command. For example, if the function has (interactive "bGive me a buffer: ") in its definition, then the function will be callable with M-x. When the user calls the function with M-x, Emacs will prompt the user for a buffer name (because of the b), and the name they type will be passed as an argument to the function.

The point of making a function a command is to make calling it easy for end-users, not just for Emacs Lisp programmers. Commands (run with M-x) are easier to run interactively in these ways:

You don’t have to surround the command name with () to make it a valid S-expression.
Arguments can be passed automatically (such as the cursor position), or you can be prompted for them so you don’t have to remember what arguments are needed.
When prompted for an argument, you can auto-complete it, because the interactive form’s code characters (like b) specify what type of input to expect.

The reason you can’t call the function set-face-attribute with M-x is that its definition does not contain an interactive form, and so set-face-attribute is not a command. You must call it as a plain function, in S-expressions. You can do that from the minibuffer with M-:, or from other places with any of the other ways of evaluating code.

Emacs Mini Manual → Concepts → Command has a short, differently-worded explanation of the difference between normal functions and commands. Relationship between Emacs functions and commands explains some details not in this answer.