I'm not sure where the distinction lies - both seem same to me :-)
If I talk to HR on Monday, take a phone screen with an engineer on Wednesday, and come on-site (or Zoom now) with 4 engineers next Monday, that’s 2 rounds and 5 interviews (or 3 and 6 if you count HR)
My experience has been that if you clear the engineering phone screen the company asks you to go through all the rest of the (4-6) interviews, even if your performance in one or more of them has been sub-par. And at least here in India the post-screen interviews are spread out over several days to 2-3 weeks - there is no "onsite" as such, even over Zoom.