Abbreviated means made shorter. We talk about an abbreviated name, an abbreviated form, an abbreviated version of a book or a film with parts taken out. It is abbreviate with -ed, used like an adjective (and also as the ordinary past form: they abbreviated the title). You will see it in school English and in careful writing. In speech, people often just say short or shortened. Though actually, an abbreviated form is not always a rushed, unofficial cut — UK is the normal short name of a country, not a lazy nickname. Do not write "the abbreviate form"; English wants abbreviated in that slot.