You are correct. The main pillar of the European Union is the common market including the free movement of goods, capital and people.
Schengen was originally a treaty outside of the framework of the EU but has since been taken over by it. There are EU countries outside of Schengen (GB, Ireland) and there are non-EU countries part of Schengen (e.g. Norway, Vatican, Switzerland). However all countries that join the EU now eventually have to join the Schengen area.
Besides Visa free travel for residents of these countries Schengen also includes a common Visa for foreigners traveling to these countries (so you only need one Visa to to travel to France and Germany) and allows the police to cross the border when perusing suspects and detain them on the other side.
Schengen was originally a treaty outside of the framework of the EU but has since been taken over by it. There are EU countries outside of Schengen (GB, Ireland) and there are non-EU countries part of Schengen (e.g. Norway, Vatican, Switzerland). However all countries that join the EU now eventually have to join the Schengen area.
Besides Visa free travel for residents of these countries Schengen also includes a common Visa for foreigners traveling to these countries (so you only need one Visa to to travel to France and Germany) and allows the police to cross the border when perusing suspects and detain them on the other side.