General terminology put into context - node.js

Question

I learned Java programming before learning any other programming languages. As I learn Node.js, I'm getting all the terminology confused. I have always thought API as a library of methods, classes, etc. that someone has built to make our lives easier. Then I learned about module, which I basically assume to be the same thing as an API(list of methods already built by someone). THEN, I learned about the Express Framework, which again, is a list of methods just like a module and an API. Moreover, the way we incorporate these features into our program is all by doing something like
Var http = require('http');
Therefore, can someone who understands the distinctions between these terms put these terms in context(examples) that could address my question.
Thanks a lot for the help.

Answer 1

A library is just a collection of numerous modules, classes, functions, etc. that are related to each other.
A framework is either a type of or a part of a library that is setup for you to build on top of rather than just call upon. And the distinction between Library and Framework can sometimes be a bit blurred.
With Express, you build upon the Application and its Router which handles incoming requests and determines when to call your code.
app.get('/', function (req, res) {
// ...
});
Though, frameworks can also span beyond code into tools. compound.js' executable is a good example of this.
A module is an individual piece of a library or framework. With Node, it's a single script file and the Object that is exported from the script.
An API is the summary/description of how you interact with the library, framework, or module.
It's usually what you'll find in documentation and is the accessible members, their name, their type, what arguments they accept, etc.
Express' API is:
express
Type: function
Named Arguments: (none)
Returns: Application
Members
listen
Type: function
Named Arguments:
name: port
Type: Number
etc.

Answer 2

This is largely an opinionated question. But I will attempt to provide the some terms commonly used by the Node community, and roughly the factual differences between them.
Module as it pertains to Node is very similar to what you would associate with a Java Library. It provides a wrapper around things that Node users find they do a lot. Frequently providing wrappers around node library functions for doing things everyone wants to do. A simple example would be a recursive file system reader, like wrench. Modules also extend to files you use to modularize your code. For example, modules aren't only installed via NPM, but separate javascript files you write as part of your code base to separate code functionality, under standard OOP practices.
require('someNPMINStalledModule')
require('./someFileInYourCodeBase.js')
both are modules. One is installed via NPM and located in node_modules directory, in the directory you launched node from. The latter example is a javascript file located in the directory you launched node from.
Then there are frameworks. At the core these do the same thing as modules, however, they are meant to be more wide spread, and really change the way you use node. In the java world frameworks like Express would be similar to things like Grails. You can still include and do everything you can do in Java, but grails wraps some things for you, and provides convenient powerful method calls for doing batches of work in a less verbose way. In the end you end up with functionally equivalent code, but Grails has allowed you to accomplish more in fewer lines of code, by generalizing the language a little more. But it still, as I said, allows you to use native code, when Grails doesn't provide the functionality you need. At the cost of this 'few lines of code' gain, you have added a layer of abstraction, additional function calls, etc. This distinction is unimportant, unless you are one who cares deeply about style. A hardcore ExpressJS developer likely wouldn't like it if you included a plain node http server in your code. Not so much because it is invalid Node, or from a perforamnce view any different, it wrecks the style of your code. If your code uses a framework, you should stick to using the coding conventions as used in this framework. But if you use a module like wrench to recursively search a directory, it is still perfectly stylistically acceptable to use fs.readFile, to read a single file.
Then there are mini applications which is a module that allow you to quickly launch simple things like serving a file. For example: http-server will server a directory of files to any port you wish, with a simple command line. You wouldn't use them in your own code with 'require' but this type of module can honestly be some of the most useful thing node provides, I highly recommend using some. (Nodemon, http-server, and grunt are a few highly useful examples of modules that can help make your development life easier)
Finally there are Native Extensions. The concurrency that Node provides comes from the V8 backend. Replicating this in pure Javscript is impossible, and the only way to write truly asyncrhonous code is to take advantage of asynchronous operations provided by the Node API, do some really wonky logic with process.nextTick, fork child processes, or write native extensions. Native Extensions provide truly concurrent operations that Node does not provide. Database communication is the most obvious example, but anyone can develope a C++ extension that will spawn threads to do work. There is also a very handy module that launches threads to handle bits of Javascript called "threads a gogo". It simplifies the launching of truly concurrent work, though if you're in a position where such things are necessary, you may find that you're using the wrong language for your use case. Ultimately these are no different from Modules in the way that you use them, but being aware of the fact that they can provide additional concurrent method for I/O type of operations not provided by NodeJS APIs is a unique and very important distinction.