Originally Posted by Aviatrix
The basic principle one needs to understand is that Schengen vs non-Schengen is about Immigration whereas EU vs non-EU is about Customs.
There are EU countries that are not part of Schengen - the UK, Ireland and all the new EU members.
There are non-EU countries and territories that are part of Schengen - Norway and the Faroe Islands are members now, Switzerland is due to join in the near future.
Excellent summary.
In addition, for our US friends,