A fetish technically refers to an attraction to an inanimate object, although this includes body parts, such as feet (like a foot fetish).
Kink means sexual activities that fall outside of sex that society traditionally considers acceptable. That can include everything from role-playing to Shibari to impact play.
Not all BDSM is fetish/kink, but all fetish/kink is BDSM... probably. Some classifications are just my opinion
