Modern and contemporary are two styles frequently used interchangeably. Contemporary is different from modern because it describes design based on the here and now.
The primary difference separating modern and contemporary design style is that modern is a strict interpretation of design that started in the 20th century. Contemporary on the other hand, is more fluid and can represent a sense of currency with less adherence to one particular style. For example, contemporary style may include curving lines, whereas modern design does not. You can refer to modern vs contemporary article for more information.