1:
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.
2:
Just to add on new information since people may continue to hit this question: Chrome has basically deprecated plugins as of March 2017 (Chrome 57). If you go to chrome://plugins now, you won't see anything (you used to see a list of installed plugins with enable-disable links like for extensions).
It seems the reasoning is that the only plugins they actually wanted to allow you to enable/disable are Flash and PDF Viewer, both of which were moved to the Settings menus (if they weren't already there, not sure). The rest are considered to be integral parts of the browser. https://www.ghacks.net/2017/01/29/google-removes-plugin-controls-from-chrome/
Makes things a bit simpler to think about now.