Being kinky usually means enhancing sexual intimacy with your partner by adding new and creative elements to sex, such as covering each other in whipped cream and licking it off. In that example, the whipped cream is secondary to the sexual experience that you and your partner create together. In other words, you could have just as much good, kinky fun by wearing Star Trek costumes or speaking in different accents.

Having a fetish, on the other hand, means that you as an individual are sexually aroused by a specific object, body part, or role-play even without a partner. A person with a fetish might masturbate while they hold, smell, rub, or taste the object, or they might ask their partner to wear it or use it during sex.
Once I read about a man, he had many wives but he only selected wife who just had her menstrual period to be with him, why? Because he had a fetish of sniffing the menstrual blood of his wife, the smell of the menstrual blood of his wife turned him on.

Short description:
Kinky is something different or fun that may be out of your norm. You like it, but sex without it is fine, too.
Fetish is a thing/item/situation etc… that you need for arousal/pleasure/climax.

Unlike kinkiness, which can change freely along with preferences, interests, and partners, fetishes tend to have deeper roots in the psychological and physiological levels of our being.