Questions on NodeJS application

does it refer to a pure server-side written NodeJS app?

Yes. Specifically it refers to apps that have nodejs backend/server.

can those client-side apps (which run in browser) be also called NodeJS app?

It depends. Certain libraries that depend on browser api (e.g navigator, window, etc) will not work. This is because those browser objects will not exists in nodejs environment. For example, jQuery will not work fully in nodejs as certain functions to do with DOM manipulation depends on the browser api. On the other hand. React can be used in both browser and nodejs because it has APIs which are compatible in both browser and nodejs environment.

Previously, if we want to use a library (e.g jQuery) we'd have to attach a corresponding script tag that points to the source. Now, you can use npm to download the library code into the node_modules folder and use it from there using require or ES6 import. But, you probably have to do some preprocessing first such as bundling your code using Browserify and Gulp. You might want to look a tutorial on how to do that here.

The unit-testing frameworks like Mocha, Jasmine, etc be used for both the types of apps I described above ? Or is it meant only for server-side NodeJS app ?

Mocha, jasmine, chai does not depend on browser or nodejs specific features so they all should work in both platforms. As for the others, you have to check if they depend on browser or nodejs specific features. If they do, the library might work in one platform (e.g browser) but not the other.

1. "Node.js" is a server-side "JavaScript" platform. That means in a NodeJS app we replaces the typical server side languages like PHP, Ruby, etc.. with the JavaScript. When it comes to frontened we have been using Javascript and its libraries like JQuery for a very long time to add behavior to our apps. But after the recent boom of SPA(Single Page Applications) we can see lots of frameworks like Angular, Ember built on JavaScript to make SPA easier.

NPM is a package manager for JavaScript which itself uses Node to perform its operations. Using NPM we can bring many JavaScript packages (that includes all the client side JS libraries) to our project. But that does not mean your's is Nodejs app if you are using NPM to install AngularJs for your ASP.net application. It is like we need Ruby gems to install SASS preprocessor.

2. That's the beauty of a pure JavaScript(NodeJS) app. We can use the testing framework in both ends. Moreover that a developer can avoid mental switching between different syntax of the two languages, and even we can reuse some code/logic in both server and client side.

npm is a package manager for javascript. Using npm to import and manage packages for your application does not make it a Node.js app.

There is no such "Node.js apps". Applications refer to the front-end/client side. You can choose Node.js or whatever on your back-end/server side, independently from your front-end.

I hope I have clarified a bit :-)