The void type signals intent. In the first example where you define a function:

function sayHello() : void { }

You are saying "this function will not return anything". However in the second example:

type say = () => void;

function callSay(func : say) { }

The "callSay" function is actually saying "I promise not to use the return value of the func". So that's why it's still OK for functions declared like this to return something:

let sayHello : say = () => { return 1; }

Whoever receives this sayHello function has already promised not to use the return type, so it does not matter if you do return something.