What are Chrome apps vs plugins vs extensions and how to develop them

To answer your first question this explains the differences between apps and extensions (I think there's no better way to explain their nature): https://developers.google.com/chrome/web-store/articles/apps_vs_extensions

What do you mean with "what kind of apps"? You can develop both hosted and packaged apps if is that what you intended, give a look at this: https://developers.google.com/chrome/apps/docs/index

Anyway the easiest way to start would be by building an extension, how-tos and good documentation makes it good to start with:

http://developer.chrome.com/extensions/getstarted.html

Just to add to the above answer which was missing difference between Plugin and Extension is:

Plugin is a third-party library that is plugged-in to the browser and allows for being embedded on a webpage. It affects only the web page that is using the plugin.

Extensions change the browser UI, add menus or change overall look of the browser and can process each page that gets loaded.

So to sum it up - plugins add functionality and extra features to a particular webpage while extensions add functionality and features to the whole browser and change the behavior of the browser.