Why was the word "brother" in verse 12 of Surat An-Nisa interpreted as meaning a brother from the mother's side, while in verse 176 of the same surah, it was interpreted as meaning a full brother or a brother from the father's side, and is this related to a Prophetic Hadith?

There is no Hadith from the Prophet, peace and blessings be upon him, stating that the siblings referred to in His (Allah’s) saying: {…and if he has a brother or a sister…} are maternal siblings. However, the Companions, may Allah be pleased with them, interpreted this verse as such, including Abu Bakr Al-Siddiq and Sa’d ibn Abi Waqqas. Scholars have unanimously agreed that the siblings in this verse are maternal siblings, based on His (Allah’s) saying: {…but if they are more than that, they share in one-third…}. Sa’d ibn Abi Waqqas used to recite: "And if he has a brother or a sister from his mother." There is no disagreement among the people of knowledge that the inheritance of full siblings (from both parents) or paternal siblings is not like this, which indicates that the siblings mentioned at the end of the Surah are the deceased’s full siblings or paternal siblings, due to His (Allah’s) saying: {And if there are brothers and sisters, male and female, then the male shall have the portion of two females.}.