The European Union was formed with the purpose of developing a single market through a standardised system of laws and regulations that could be applied equally in all member states.
The origin of what we know as the European Union today can be traced back to the Treaty of Paris, signed in 1951 and the Treaty of Rome in 1957. These paved the way to what we know as the EU. The original members of the European Coal and Steel Community and the European Economic Community. The original members were Belgium, France, Italy, Luxembourg, the Netherlands, and West Germany.
The European Union was formally established in 1993 during the Maastricht Treaty. Today the EU is a unified trade and monetary body composed of 28 member states. This will change once the United Kingdom finishes its transition and leaves the EU.
The Schengen Zone is a result of the Schengen Agreement which was first signed in 1985 with the purpose of abolishing internal borders between its member countries. Initially, it was signed only by five members. Currently the Schengen Zone is made up of 22 EU member states and the four members of the EFTA (European Free Trade Association).
The difference is that the Schengen Zone was established to encourage the free movement of people, goods, and businesses.