How does it differ from the Kagyu school?
Mainly it is just difference in lineage. Result is the same.
There are philosophical difference since Sapan did not believe in the pointing out instructions...
Sure he did, he just felt is needed to be based on having already received the four full empowerments.
Sapan did not accept sutra mahāmudra as such -- but he opined that Mahāmudra could be realzied through either the two stages or through Guru Yoga.
but thought the great seal depended on initiation into a full Mandala. Sapan thought Mahamudra was totally free of concepts but criticized Gampopa's Mahamudra as just creating greater clarity and calm. He considered any sutra based non-tantric great seal to be impossible. Mahamudra in Sakya is depended on complete initiation into the Hevajra tantra. Now the Tsarpa Sakya I have been told do believe in pointing out instructions, but in general the Ngor and Khon lineages do not. So those are the major differences that I am aware of.
Vajrayogini has had a mahāmudra pointing out instruction from the beginning. It is in Jetsun Dragpa Gyaltsen's collected works. Therefore, the Ngor and Khon Lineages accept pointing out.
As you probably know, I was a Sakya pracitioner for many years.
As for the disctinction between the inseperability of clarity of the three visions and emptiness and sutra mahāmudra, this is just fighting over a name. The meaning of the two is the completely identical.