Your college selects students for HSF (ours is based entirely on class rank) while A&O is personal application (no role played by college). Pretty much the same, but A&O does have decent cv value particularly with rank obsessed firms.
These are short term courses offered by these firms to selected students from certain NLUs. Originally to the trifecta NLS, NALSAR, NUJS. Later NLUD was also included. I think NLUJ has been too, not sure about the rest.
HSF ILP is being hosted at Jindal this year. They have sent invitations to all top NLUS (NLS, NALSAR, NLUJ, NLUD, GNLU, NUJS). Only NLS and NALSAR have confirmed that their students will be participating. NLUJ, NUJS, NLUD, and GNLU did not respond to the invitations.
Both are prestigious, and give an instant recognition that you may be a viable candidate for corporate law firms - I attended the HSF ILP, and interviewers were impressed during Day Zero (as it is a reflection of rank+corp law research+moots etc.)
Yes, have attended both and can safely say that A&O one is quite extensive and there is a massive learning curve. From International Project Finance, to International Debt Finance to Capital Markets in the US, they covered a lot of themes that were perfect, if you are planning to apply to any Vacation Schemes. Choose A&O or try to get in. I think they were planning to discontinue HSF-ILP this year onwards, someone confirm
A&O is reserved only for NLS, NALSAR, NUJS, NLUJ and NLUD (I may be wrong)
Try to apply for both if you get the opportunity!