Snobbery is the action of a person who thinks he or she is more important or worthwhile than others. The plural form is snobberies.
A person who thinks or acts this way is called a snob. Something can be snobby, snobbier, or the snobbiest.
Another adjective form is snobbish. The adverb form is snobbishly. And the back-formation noun from the adjective is snobbishness.
So in the end, snobbery and snobbishness are synonyms for the same type of behavior.