This term is used interchangeably in everyday conversation but there is a big distinction if we want to get technical.
Cement, or more commonly referred to as Portland cement due to its popularity, is a flour-like mixture of limestone, calcium, silicon, aluminium, iron and other ingredients. These raw rocks are crushed and heated in a kiln to 2700 degrees Fahrenheit. The finished mixture would trigger chemicals reactions to harden when water is added. Cement is one of the basic recipe to make concrete.
Concrete is a mixture of cement with rocks, sand and crushed stones, or collectively referred to as aggregates. Typical mixture ratio of concrete would contain around 15% of its weight from cement. Upon mixing with water the cement begins to hardens and set. At this time the mixture can be poured into molds for a specific shape.
In essence, different types of concrete exist to serve different purpose. The general rule of thumb is that the strength of the concrete is inversely related with the amount of water added. You might need a stronger concrete for your driveway's concrete slab compared to concrete used for patio floors.