Does the word Al (Arabic: آل) indicate consanguineous relevancy or support?

I'm reading Syed Husain Mohammad Jafri's "The Origins and Early Development of Shi’a Islam ". On the term "Al" he mentioned: >The term Al, meaning nearer or nearest relations by descent from the same father or ancestor or a man's family or kinsmen, is used in the Qur'an twenty-six times in connection with the descendants of the prophets or those who succeeded them in guidance and special favour from God. A verse describing Muhammad as belonging to the descendants of Abraham has been quoted above. In another verse (IV, 54) we read: "Or do they envy the people for what God has given them of His grace: But indeed we have given to Abraham's children (Al Ibrahim) the book and the wisdom and we gave them a great kingdom." And about "Ahl": >The word Ahl, which is used many times in the Qur'an has almost the same meaning as Al, though it is also used in a broader sense in referring to the people of a town or inhabitation, a group, or followers. When used in conjunction with the term bayt: Ahl albayt, it refers to the immediate descendants of a family or such a family of the same "house", or bayt. In this compound form, Ahl al-bayt is used in the Qur'an especially in reference to the immediate family of Muhammad. In verse XXXIII, 33, we hear: "And God only wishes to remove from you [all kinds of] uncleanliness, O members of the family [of Muhammad] and thoroughly purify you." Jafri claims here that the word Al "is used in the Qur'an twenty-six times in connection with the descendants of the prophets or those who succeeded them", when I tried to search in the Quran for different stems of the word "Al ", most of which did not indicate "connection with the descendants of the prophets or those who succeeded them" but mostly indicated being a proponent of someone that might be even a Kafir like Muse's Pharaoh (for example see Quran 1:50 and Quran 54:41), however, some of the occurrences did indicate relatives like Lot's Al (Quran 15:59), however this can be interpreted as proponents too since Lot's family were the only followers of his. How should Al be exactly interpreted? When we say "Al-Albayt" we probably refer to Ahl al-Kisa or someone who was related to the Prophet, but does this apply when we say "Al-Muhammed" like in Tashahhud or it mean the proponents of Muhammed in the latter?