Sometimes, we confuse "contemporary" with "modern." Christopher Porikos, an Interior Designer based in the Los Angeles area, writes "Contemporary design really means or references design that is happening now."
"Modern design is mainly looked as sterile and sometimes cold by some.
There is a common thread of metal, glass and leather. Hard surfaces
like marble and concrete for flooring are used as well as simple high
gloss surfaces for the kitchen and bathrooms."
I laughed to myself when I realized an easy way to remember the difference. Assume you are living in the time of Downton Abbey. The designs in the show appear to us as very traditional, but to them it was contemporary. Modern would still be modern.