Up until the late '80s-early '90s cars and rules were rather similar, and drivers like Andretti or Mansell were able to move between categories with relative ease.

I'd say that the rift become apparent in '94, after the safety changes introduced due to Senna's Death and the massive shift in pilot training brought by Michael Schumacher.

The Indy 500 was actually part of the official Formula 1 calendar from 1950 to 1960, though the two series diverged after that.

Some Indy features (refueling, changing tires even if they didn't have a puncture, safety cars) got adopted by F1 through the 1980s, specially as F1 started to lose audience to the American series in the early 1990s.