All Sadaat are the progeny of Rasūlullāh ﷺ (Aal-e-Rasool ﷺ), but all Sadaat are not Ahl al-Bayt. However, all Sadaat are the close relatives (Zil Qurba). In the Holy Quran, Allah the Exalted and Glorious says:
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قُل لَّا أَسْأَلُكُمْ عَلَيْهِ أَجْرًا إِلَّا الْمَوَدَّةَ فِي الْقُرْبَىٰ**

Say, “I do not ask any fee from you upon this, except the love between close ones”

The application of this verse extends to all the progeny of Rasūlullāh ﷺ (Aal-e-Rasool ﷺ). The descendants of Ali رضي الله عنه , the descendants of Jafar رضي الله عنه , the descendants of Aqeel رضي الله عنه , the descendants of Abbas رضي الله عنه , and the descendants of Harith رضي الله عنه are all included in this. Sadaqah Zakat are forbidden (Haram) for all of them.
All Sadaat are from Aal-e-Rasool ﷺ. However, the term Ahl al-Bayt specifically applies to the pure wives (Azwaj-e-Mutahharat) and the daughters of the Messenger of Allah ﷺ. Furthermore, Maula Ali, Imam Hasan, and Imam Husain رضي الله عنهم are included in the Ahl al-Bayt, and the honorary member of the Ahl al-Bayt is Hazrat Salman Farsi رضي الله عنه

والله ورسوله أعلم

[Translated by] Faqeer Muhammad Junaid Raza

Begger at the Doorsteps of Scholors