Is a closure only created when a inner function returns something? [duplicate]

Question

I have been playing around with closures a little bit and I have a difficult time understanding what's the difference between lexical scoping and closures.

In the examples below both child functions are able to reach the a variable thanks to lexical scoping. Now I wonder where exactly is the closure created in the second example? Is it because of the childFunc() being returned directly, or is it because of childFunc() being stored in a seperate child variable before being exectuted?

Example 1: No closure

function parentFunc() {
    let a = 10;

    function childFunc() {
        console.log(`hey from child func Mr. ${a}`);
        a++;
    }
    childFunc();
}
console.dir(parentFunc) //closure not part of the Scopes

parentFunc() //doesn't increment a
parentFunc()

Example 2: Closure

function parentFunc() {
    let a = 10;

    return function childFunc() {
        console.log(`hey from child func Mr. ${a}`);
        a++;
    }
}
const child = parentFunc()
child(); // increments a
child();

console.dir(parentFunc) //closure is part of the scopes