Yes, Chrome Apps can make use of the Chrome Platform API which allows them to do all kinds of privileged things (if the required permissions were given).

http://developer.chrome.com/apps/api_index.html

So... yea, it's very similar. Both are some sort of web-related runtime which can be used for all kinds of applications thanks to additional APIs which make the environment less restrictive.

No. This is a development environment, not a runtime.