The first four categories in the original list are: الْفَاعِلُ، وَمَفْعُولُ مَا لَمْ يُسَمَّ فَاعِلُهُ، وَالْمُبْتَدَأُ، وَالْخَبَرُ.
Translation: The fāʿil, the patient of a verb whose doer is not named (the nāʾib al-fāʿil), the mubtadaʾ, and the khabar.
مفعول ما لم يسم فاعله is the noun raised with a passive verb; it is commonly called نائب فاعل. Example: ضُرِبَ زَيْدٌ — “Zayd was struck.” Here زَيْدٌ is nāʾib al-fāʿil.
The مبتدأ is the noun about which a nominal sentence begins, and the خبر tells us something about it: زَيْدٌ قَائِمٌ — “Zayd is standing.”