When and why to use these various Java Script function declaration formats?

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What are the differences between the following function declaration formats? When is it more correct to use which?

From a beginner's perspective, and a high level (non-deep) point of view, they all three appear to work the same - hence it makes things feel confusing and demands the question.

1.

const counter1 = function(num) {
    var x = 0;
    while (x < num) {
        console.log(x);
        x ++;
    };
    return 0;
};

2.

function counter2(num) {
    var x = 0;
    while (x < num) {
        console.log(x);
        x ++;
    };
    return 0;
};

3.

const counter3 = (num) => {
    var x = 0;
    while (x < num) {
        console.log(x);
        x ++;
    };
    return 0;
};

All of them appear to behave the same.

1

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There are more than a few differences between your three examples actually.

So, for one, you have to be careful using const for your function declarations.

counter1(5); // counter1 is undefined, this will fail
const counter1 = function(num) {
    var x = 0;
    while (x < num) {
        console.log(x);
        x ++;
    };
    return 0;
};

Whereas the function will be hoisted and available for use (Edit: technically let and const are also hoisted, but they aren't initialized so you cannot access them before they are declared, more info here.

counter2(5); // works fine
function counter2(num) {
    var x = 0;
    while (x < num) {
        console.log(x);
        x ++;
    };
    return 0;
};

Also note that const prohibits reassigning the variable, so you couldn't go say const counter1 = {} later down the line, whereas you could feasibly do so with the function example.

As far as the difference between function(num) { versus (num) => {, well in your example it makes no difference. But there are some differences... for example

const thisWillFail = () => {
    console.log(arguments.length);
};
const thisWorks = function() {
    console.log(arguments.length);
};

If you're unfamiliar with the arguments object, you can find info here.