Al-Kalalah and the pertinent verses; 4:12 and 4:176
The use of Al-Kalalah here has created a lot of confusion and even Yusuf Ali chooses to interpret one as dealing with uterine siblings only and the other as paternal siblings. He didn't invent this as this can be found in Lisanul-Arab as one of the interpretations of these two verses. Ibn Mandhur essentially gives a tafsir with this meaning with the following:
فجعل الكَلالة ههنا الأُخت للأَب والأُم والإِخوة للأَب والأُم، فجعل للأُخت الواحدة نصفَ ما ترك الميت، وللأُختين الثلثين، وللإِخوة والأَخوات جميع المال بينهم، للذكر مثل حَظِّ الأُنثيين، وجعل للأَخ والأُخت من الأُم، في الآية الأُولى، الثلث، لكل واحد منهما السدس، فبيّن بسِياق الآيتين أَن الكَلالة تشتمل على الإِخوة للأُم مرَّة، ومرة على الإِخوة والأَخوات للأَب والأُم
This states: "He (God) has made (the inheriting siblings for) Al-Kalalah here the sister from one's mother and father and siblings from one's mother and father (in general). He gave half to the lone sister and 2/3 for the sisters (to share) if they are more than one. For male and female siblings all of the wealth (is to be shared) between them with the male's share being double that of the female. He (God) gave the (lone) maternal brother or sister in the first verse (that mentions Al-Kalalah) a third and (he gave them) a sixth for each if they are two of them. In the context of both verses Al-Kalalah pertains to the maternal siblings in one place and siblings from both the deceased's mother and father in the other place."
This is a tafsir of why Al-Kalalah is different in one verse and different in another and not a definition of al-Kalaalah.
The most pertinent definition of Al-Kalalah is the following:
واختلف أَهل العربية في تفسير الكَلالة فروى المنذري بسنده عن أَبي عبيدة أَنه قال: الكَلالة كل مَنْ لم يرِثه ولد أَو أَب أَو أَخ ونحو ذلك
This says that the scholars of Arabic have differed about the explanation of Al-Kalalah but Al-Mundhiri related, using Abu 'Ubaydah as support, that: Al-Kalalah refers to anyone whose son OR Father OR brother doesn't (exist to) inherit him.
What has caused confusion with the term is that most understandings understand Al-Kalalah as one who is left without both a parent and a child as an inheritor. But if one has a parent and no child or a child and no parent or any combination of missing parent, child or sibling then all of these can be considered Al-Kalalah.
Given the specification of 4:176 specifying no children in addition to Al-Kalalah and it allowing a brother to inherit the full inheritance of his sister it would seem that Al-Kalalah here and in 4:12 is talking about Al-Kalalah where there is no parent to inherit. When there is no child to inherit the Quran just says 'laisa lahu walad.' So in 4:12 there are children and the Al-Kalalah mentioned refers to no parents as inheritors and in 4:176 again the Al-Kalalah refers to no parent inheritors, while specifying in addition to the term that there are no children to inherit either. This explains why there is less for the siblings in 4:12 and more for them in 4:176.
I hope this has provided some clarification to this very confusing issue which at face value seems to present the Qur'an as contradicting itself, and which can get even more confusing given the more popular meaning of the word and the various subtleties of of the term.