Technically only non-essential services and personnel are closed. However, since the USG has in recent decades expanded the definition of "essential" to almost everybody, 85% of government activities are still being funded as usual. This is just propaganda and manipulation. A show, so to speak.
Here's an article on the topic
http://www.zerohedge.com/news/2013-10-03/government-shutdown-36-facts-which-prove-almost-everything-still-running