What is the difference between the pillars (arkān) of prayer, its obligations (wājibāt), and its recommended acts (sunan)?

The Sunan (recommended acts) of prayer are those acts other than the Arkan (pillars) and Wajibat (obligatory acts). Prayer is not invalidated by omitting any of them, even intentionally, unlike the Arkan and Wajibat. A Rukn (pillar) is not dropped, whether intentionally or by forgetfulness, whereas a Wajib (obligatory act) is dropped by forgetfulness and compensated for by the prostration of forgetfulness (Sujud al-Sahw).

The Arkan (Pillars) of Prayer (14): Standing (for those who are able), Takbirat al-Ihram (the opening Takbir), reciting Al-Fatiha, bowing (Ruku‘), rising from bowing, standing erect after bowing, prostrating (Sujud), rising from prostration, sitting between the two prostrations, Tum’aninah (tranquility/stillness in each posture), the final Tashahhud, sitting for the final Tashahhud and for the two Taslims, the two Taslims (saying As-salamu alaykum wa rahmatullah to the right and left), and observing the correct sequence of these pillars.

The Wajibat (Obligatory Acts) of Prayer (8): Saying Takbir (God is Greatest) other than Takbirat al-Ihram, saying "Allah hears those who praise Him" (Sami‘a Allahu liman hamidah), saying "Our Lord, to You be all praise" (Rabbana wa laka al-hamd), saying "Glory be to my Lord, the Most Great" (Subhan Rabbi al-Adhim) once in bowing, saying "Glory be to my Lord, the Most High" (Subhan Rabbi al-A'la) once in prostration, saying "My Lord, forgive me" (Rabb ighfir li) between the two prostrations, the first Tashahhud, and sitting for the first Tashahhud.

The Sunan (Recommended Sayings) of Prayer (11): The opening supplication (Du‘a al-Istiftah), seeking refuge (from Satan - Ta‘awwudh), uttering Basmalah (Bismillah ar-Rahman ar-Rahim), saying Ameen, reciting a surah after Al-Fatiha, the Imam reciting aloud, saying "filling the heavens and filling the earth and filling whatever else You wish" (for one not praying behind an Imam), repeating the glorification in bowing more than once, repeating the glorification in prostration more than once, repeating "My Lord, forgive me" more than once, and sending blessings upon the Prophet and his family and supplicating after the final Tashahhud.

The Sunan (Recommended Actions): Raising the hands in the specified positions, placing the right hand over the left, looking at the place of prostration, separating the feet, grasping the knees, ensuring the prostration organs are firm on the ground, Mujafah (keeping the arms away from the sides during prostration), Iftirash (sitting posture) and Tawarruk (sitting posture), placing the hands on the thighs with specific details about the fingers' posture, and turning the head to the right and left during the Taslim.