Modern Interior decor vs Contemporary Interior decor

Often these terms are used together or interchanged. However, they are not the same thing. Depending on whom you are speaking to, if you ask a piece of furniture that is Modern and then ask that same person for a piece of furniture that is contemporary you could get very different pieces of furniture. Some will use these terms interchangeably due to one common thread in these two designs- clean lines and uncluttered look. You will not see lots of accessories in either style. They are both minimalistic designs. However, Modern normally refers to a certain period of time back to the end of the 19th century. At this time (in terms of interior design) people adopted the look of minimalism and clean lines instead of more ornate styles such as Victorian where you would fine lots of carved detail, fussy prints, lace and color. 

Contemporary would normally be used to describe "new".  Not to say that it would not be reflective of Modern design but new. Contemporary also would most likely use more colors in a warmer way as Modern would feel colder. 

Example of Modern decor

Example of Contemporary decor