The Schengen Area refers to a treaty that allows broad freedom of movement for European citizens between Schengen countries without the need for a visa. Use to discuss the politics of countries joining/leaving the Schengen Treaty
Schengen (so called for the Luxembourg town where it was signed) allows for the free movement of European citizens across borders without the need for a visa. It also created a Schengen Visa for visitors, meaning you only need one visa to travel most of Europe. It was largely engineered by the european-union, but there are EU members who are not in Schengen and vice versa.
The EU has published this video that describes, the benefits of Schengen