You have described everything precisely. The only thing that I would add is that for the two different "castes" within the H1B system that you have identified, there's one other difference.
People who are working for Apple, Microsoft, Intel etc are using H1B as a gateway to a green card, and ultimately to citizenship - which they can do, because H1B is explicitly "dual intent", so you can apply for a green card without getting kicked out of the country; and because there's a specific process whereby employer sponsors the employee for a green card. This isn't to say that every single H1B working for these companies will do that - but the majority will. The companies in question are generally interested in retaining employees long-term, so they do sponsor any employee who asks for green card (in fact, they will proactively push you to apply if you don't do so yourself), and will provide lawyers to handle the application for you, pay various fees etc.
People who are working for Tata, Infosys etc are not there for citizenship. It's not that they wouldn't want to - it's that those companies will generally not sponsor them. So it's really just a gig to come work in US and earn a lot of money (comparatively to what they could earn at home), and then come back rich, and with a US job on your resume.