메뉴판에 best라고 되어 있는 메뉴가 가장 인기 가 많아요. The menu ""said"" best in the menuboard is the most popular. In Korea, we don't say "something says: the signs says like that blah blah.." We feel very weird when the subject in the sentence is not someone unless it's inevitable to use something as a subject. So, we'd 1) make the sentence passive voice or 2) change its subject to someone. 메뉴판에서 best라고 말하는 메뉴가 있다 X 1) 메뉴판에 best라고 쓰이어 있는[쓰여 있는/써있는] 메뉴가 있다. 2) cannot choose it because we wanna describe the menu.

yes, it's just abbreviated forms.