What is the difference between require(‘mypackage.js’) and require(‘mypackage’)?

Here is the answer:

Module.prototype.load = function(filename) {
  debug('load ' + JSON.stringify(filename) +
        ' for module ' + JSON.stringify(this.id));

  assert(!this.loaded);
  this.filename = filename;
  this.paths = Module._nodeModulePaths(path.dirname(filename));

  var extension = path.extname(filename) || '.js';
  if (!Module._extensions[extension]) extension = '.js';
  Module._extensions[extension](this, filename);
  this.loaded = true;
};

1. Node.JS looks to see if the given module is a core module. (e.g. http, fs, etc.)
   Always takes the precedence in the loading modules.
2. If the given module is not a core module (e.g. http, fs, etc.), Node.js will then begin to search for a directory named, node_modules.
   It will start in the current directory (relative to the currently-executing file in Node.JS) and then work its way up the folder hierarchy, checking each level for a node_modules folder.
   Once Node.JS finds the node_modules folder, it will then attempt to load the given module either as a (.js) JavaScript file or as a named sub-directory; if it finds the named sub-directory, it will then attempt to load the file in various ways. So, for example
3. If you make a request to load the module, “utils” and its a directory not a .js file then:
   Node.JS will search a hierarchical directory for node_modules and
   utils in the following ways:
   
   ./node_modules/utils.js
./node_modules/utils/index.js

./node_modules/utils/package.json
4. If Node.JS still can’t find the file in above steps, Node.js will then start to look into the directory paths from environment variables i.e. NODE_PATH set on your machine(obviously set by Node.JS installer file if you are on windows)
   Not Found in all the above steps then, prints a stack trace to stder
   E.g.: Error:Cannot find module 'yourfile'
   
   For more information: link is here even the cyclic require() is explained very well.