In JavaScript, an async function is a function that allows you to write asynchronous code using the await keyword. It enables you to write cleaner and more readable code when dealing with asynchronous operations like fetching data from an API or reading/writing files.

Inside an async function, you can use the await keyword to pause the execution of the function until a promise is resolved or rejected. This makes it easier to work with promises and handle asynchronous operations in a more synchronous-like manner.

Here's an example of an async function in JavaScript:

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async function fetchData() {
  try {
    const response = await fetch('https://api.example.com/data');
    const data = await response.json();
    console.log(data);
  } catch (error) {
    console.log(error);
  }
}

fetchData();

In this example, the fetchData function is declared as async. It uses the await keyword to pause the execution and wait for the fetch request to be resolved before moving on to the next line of code. This helps to ensure that we have the data before attempting to log it to the console.

Note: The use of async functions requires support for Promises, which is available in modern JavaScript environments.

A callback function is a function that gets passed as an argument to another function and is executed at a later time or when a certain condition is met. It is like giving someone your phone number and asking them to call you back when they are ready. In programming, callbacks are commonly used in asynchronous operations, like fetching data from a server or performing animations, where the function needs to wait for a response or an event to happen before continuing with the rest of the code.

Here's an example in JavaScript:

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function getDataFromServer(callback) {
  // Simulating an asynchronous operation
  setTimeout(function() {
    const data = { id: 1, name: "John Doe" };
    callback(data);
  }, 3000);
}

function displayData(data) {
  console.log("Received data:", data);
}

getDataFromServer(displayData);

In the example above, the getDataFromServer function takes a callback as an argument and simulates fetching data from a server. After 3 seconds, it invokes the callback with the fetched data as the argument. The displayData function is passed as the callback and is responsible for displaying the received data.

A callback function is a function that is passed as an argument to another function and is executed at a later point in time. It is commonly used in event-based programming or asynchronous operations. When the event or operation is completed, the callback function is called to handle the result or perform additional tasks.

For example, in JavaScript, the setTimeout function can take a callback function as its first argument. This callback function will be executed after the specified delay:

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setTimeout(function() {
   console.log('This is a callback function!');
}, 2000);

In this example, the anonymous function is the callback function that will be executed after a delay of 2000 milliseconds (2 seconds). When the delay is complete, the message "This is a callback function!" will be printed to the console.