مصدر المرة is a verbal noun that is used to indicate the number of times the subject did the verb in question. The word itself is singular and indicates doing the action once, hence its name: مرّة = once. You can make this noun dual or plural to indicate doing it more than once. One of its most common patterns is فَعْلَة, such as جَلْسَة. Its dual is جَلستان, and its plural is جَلسات.
مصدر الهيئة is a verbal noun that is used to indicate the manner in which the subject did the verb in question. It can only be derived from verbs whose base form has three letters (not more). Its pattern is فِعْلَة, such as جِلْسَة. For example: جلس جِلسة الملوك = He sat in the manner of kings / He sat the way kings sit.