Schools of thought (madhabs)
Hanafi inheritance
The largest Sunni school. The grandfather blocks the siblings outright, and full siblings get nothing in the Musharakah case.
The Hanafi school is the largest by following. Historically the school of the Ottoman empire, today it's dominant across South Asia, Central Asia, Turkey, and the Levant. On inheritance it agrees with the other three schools in most cases and differs on a few specific points.
Where Hanafi differs
Grandfather blocks siblings
In the Hanafi school, a paternal grandfather completely blocks the deceased's siblings (full and paternal half) when the father is dead. The other three Sunni schools have him share with the siblings using the grandfather-with-siblings calculation.
No Musharakah
In the Musharakah case (husband + mother + 2+ maternal half-siblings + full siblings), Hanafi gives the full siblings nothing. They're residuary heirs, and the fixed shares have already used up the estate. Maliki and Shafi'i let them join the maternal half-siblings in the 1/3 share.
Father blocks maternal grandmother
Only in the Hanafi school does the deceased's father block the maternal grandmother. Other schools allow her to inherit her 1/6 even when the father is alive.
What it has in common with the others
Everything else: the six fixed fractions, blocking by closer descendants, Awl, Radd (Hanafi applies it readily, even more so than Maliki), and Umariatan.