Is a callback also known as a higher-order function?

Question

I'm trying to understand callback and higher-order functions but there's a description from a blog post, Understand JavaScript Callback Functions and Use Them, that confuses me, the implication being that they are one and the same:

A callback function, also known as a higher-order function,...

It was repeated verbatim on a Quora answer to the question asking about What is a simple explanation of higher order functions and callbacks in JavaScript?.

It doesn't make sense to me. From what I understand, a higher-order function takes in or returns other functions and a callback function is the function being passed/taken in, so how can it be both at the same time? Is there something that I'm not understanding about that description?

Answer 1

Callback function

A callback function is a function passed into another function as an argument, which is then invoked inside the outer function to complete some kind of routine or action.

Return a function

A function that returns a function called Higher-Order Function

A callback function is not a Higher-Order Function, unless it is a function that returns a function.

Simple callback:

function toto(callback){
  /** some routine or action before */
  callback();
}

function foo(){
  console.log("I'm a simple callback");
}

toto(foo);

Simple Higher-Order Function

function toto(){
  console.log("I'm a simple Higher-Order Function")
  return function(){
     console.log("I'm the return function");
  }
}

//first log
const func = toto();
//second log
func();

Callback that is also a Higher-Order Function:

function toto(callback){
  /** some routine or action before */
  const func = callback();
  func();
}

function foo(){
  console.log("I'm a callback and Higher-Order function");
  
  return function(){
    console.log("Do something...");
  };
}

toto(foo);