What is the difference between EU, Eurozone and Schengen?

The following video link (in hindi) explains the difference in EU, Eurozone and Schengen in details:

https://www.youtube.com/watch?v=lv3KQezTXuA

Also, the following text brings the main points of the each term.

EU - European Union

The European Union (also known as "EU") is a political and economical union of 28 member states that are primarily located in Europe. EU has developed an internal single market through a standardised system of laws that apply in all member states.

EU policies aim to ensure the free movement of people, goods, services, and capital within the internal market, enact legislation in justice and home affairs, and maintain common policies on trade, agriculture, fisheries, and regional development.

For more details, refer to:  https://en.wikipedia.org/wiki/European_Union

Eurozone

The Eurozone, officially called the "Euro Area", is a monetary union of 19 of the 28 European Union (EU) member states which have adopted the Euro (€) as their common currency and sole legal tender. The monetary authority of the eurozone is the Eurosystem.

The other nine members of the European Union continue to use their own national currencies, although most of them are obliged to adopt the euro in the future.

The eurozone consists of Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Portugal, Slovakia, Slovenia, and Spain.

Other EU states (except for Denmark and the United Kingdom) are obliged to join once they meet the criteria to do so. No state has left, and there are no provisions to do so or to be expelled. 

Andorra, Monaco, San Marino, and Vatican City have formal agreements with the EU to use the euro as their official currency and issue their own coins. 

Kosovo and Montenegro have adopted the euro unilaterally, but these countries do not officially form part of the eurozone and do not have representation in the European Central Bank (ECB) or in the Eurogroup.

The ECB, which is governed by a president and a board of the heads of national central banks, sets the monetary policy of the zone. The principal task of the ECB is to keep inflation under control. 

For more details, refer to: https://en.wikipedia.org/wiki/Eurozone

Schengen Area

The Schengen Area is an area comprising 26 European states that have officially abolished passport and all other types of border control at their mutual borders.

The area mostly functions as a single country for international travel purposes, with a common visa policy. The area is named after the “Schengen Agreement”. States in the Schengen Area have strengthened border controls with non-Schengen countries.

Twenty-two of the twenty-eight European Union (EU) member states participate in the Schengen Area. Of the six EU members that are not part of the Schengen Area, four – Bulgaria, Croatia, Cyprus, and Romania – are legally obliged to join the area, while the other two – the Republic of Ireland and the United Kingdom – maintain opt-outs.

The four European Free Trade Association (EFTA) member states, Iceland, Liechtenstein, Norway, and Switzerland, are not members of the EU, but have signed agreements in association with the Schengen Agreement.

Three European microstates – Monaco, San Marino, and the Vatican City – can be considered de facto participants.

For more details, refer to: https://en.wikipedia.org/wiki/Schengen_Area