How do we differentiate between the hadiths that indicate the pillars of prayer, the hadiths that indicate its obligations, and the hadiths that indicate its Sunnah acts, despite all of them being hadiths?

The jurists have divided prayer into pillars (arkan), obligatory acts (wajibat), and sunnah acts. A pillar is that which, if left intentionally or unintentionally, invalidates the prayer and is not waived under any circumstances. Examples include the opening takbir (takbirat al-ihram), reciting Al-Fatiha, standing, bowing, prostrating, rising from bowing, the final tashahhud, sitting for it, the salutation (taslim), and maintaining order. As for an obligatory act, it is waived by forgetfulness and compensated for by the prostration of forgetfulness (sujud al-sahw). As for a sunnah act, prayer is not invalidated by leaving it, whether intentionally or unintentionally. The madhhabs (schools of thought) differ in specifying the pillars and obligatory acts. However, according to the Shafi'i madhhab and the majority of scholars, glorification (tasbih) and all other remembrances in bowing and prostrating, saying: "Allah hears those who praise Him," and "Our Lord, to You be praise," and the takbirs other than the opening takbir, are all sunnah and not obligatory.