I would like to know if there is any difference between Einkaufszentrum and Kaufhaus? Is one maybe bigger than the other?
A "Kaufhaus" sells all kinds of goods but most departments belong to the same company. The "Kaufhaus" as a whole pays rent for the building and all employers get their salary from the "Kaufhaus" So a person working in the kids section might have to fill in in cosmetics some days. A famous example in German is the Galeria Kaufhof at Berlin Alexanderplatz.
An "Einkaufszentrum" is basically a building in which different stores can rent retail space. Each store has their own employers who have nothing to do with the "Einkaufszentrum". As the other answer says, this is pretty much a mall.
Kaufhaus = department store
which looks like one owner has all those different departments while in reality today some of the parts are operated by external comapnies.
Einkaufszentrum = shopping mall
Many different independent shops in a building or building complex.
Yes there is a difference. Kaufhaus is more like a supermarket where Einkaufszentrum is like a mall with many different shops.