A mushtarak term is established for more than one distinct meaning. The term “qur'” is a central example, with menstrual periods and periods of purity as possible senses. The existence of two dictionary meanings does not make both intended simultaneously in a single use.
When sound contextual and juristic arguments favor one sense, the result is mu'awwal. A meaning established by preference is not the same as wording from which every alternative has been conclusively excluded.