The one common trait between Node.js, AJAX, and jQuery is that all of them are the advanced implementation of JavaScript. However, they serve completely different purposes.
Node.js : It is a server-side platform for developing client-server applications. For example, if we’ve to build an online employee management system, then we won’t do it using client-side JS. But the Node.js can certainly do it as it runs on a server similar to Apache, Django not in a browser.
AJAX (aka Asynchronous Javascript and XML) : It is a client-side scripting technique, primarily designed for rendering the contents of a page without refreshing it. There are a no. of large companies utilizing AJAX such as Facebook and Stack Overflow to display dynamic content.
jQuery : It is a famous JavaScript module which complements AJAX, DOM traversal, looping and so on. This library provides many useful functions to help in JavaScript development. However, it’s not mandatory to use it but as it also manages cross-browser compatibility, so can help you produce highly maintainable web applications.