Introduction

Both CommonJS and AMD are JavaScript module definition APIs that have different implementations.

RequireJS implements the AMD API.

CommonJS is a way of defining modules with the help of an exports object, that defines the module contents. An implemention is in Node.js.

More details

RequireJS

RequireJS implements AMD, which is designed to suit the browser environment. Apparently AMD started as an offspin of CommonJS Transport format and evolved into its own module definition API. Hence the similiarities between the two. The new thing in AMD is the define() function that allows the module to declare its dependencies before being loaded. For example the definition could be:

define('module/id/string', ['module', 'dependency', 'array'], 
function(module, factory function) {
  return ModuleContents;  
});

RequireJS, while being an AMD implementation, offers a CommonJS wrapper so CommonJS modules can almost directly be imported into use with RequireJS.

define(function(require, exports, module) {
  var someModule = require('someModule'); // in the vein of node    
  exports.doSomethingElse = function() { return someModule.doSomething() + "bar"; };
});

CommonJS

CommonJS is a way of defining modules with the help of an exports object, that defines the module contents. Simply put a CommonJS implementation might work like this:

// someModule.js
exports.doSomething = function() { return "foo"; };
 
//otherModule.js
var someModule = require('someModule'); // in the vein of node    
exports.doSomethingElse = function() { return someModule.doSomething() + "bar"; };

Basically CommonJS specifies that you need to have a the require() function to fetch dependencies, the exports variable to export module contents and some module identifier (that describes the location of the module in question in relation to this module) that is used to require the dependencies. CommonJS has various implementations, for example Node.js.

CommonJS was not particularly designed with browsers in mind, so it doesn't fit to the browser environment very well. Apparently this has something to do with asynchronous loading etc.

Reference