From PMBoK, coordinator have a bit more decision making power versus expediter however they both are present in Functional as well as Weak-Matrix organization. Now if question is about expeditor/coordinator and among available options following two are there:
Is it correct to say expediter belongs to Functional and coordinator belongs to Weak-Matrix?
You need to refer to PMBOK v5.
My understanding is that Coordinator has some decision making authority while expeditor has none.
Weak matrix - PM will have no power and could essentially play the role of a coordinator but not expeditor. PM is part time, has no administrative staff and no control over budget.
Strong Matrix - PM lot of power, Full time, has administrative staff and controls budget.
Balanced Matrix organizations - power and authority are shared between the Functional manager and the Project manager. PM is full time but has part time admin staff under him. Communication is complex because of dual managers.
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