Originally Posted by Homebrew01

Chains are cross-compatible, as long as they are the same "speed"

Originally Posted by Shimagnolo

There was a period (IIRC 8-speed) when Shimano was inexplicably doing both IG and HG at the same time in the same speeds.
One of the differences was that IG & HG chains were different widths.
(IIRC the IG was narrower).
So back then it made a difference, but once 9sp came along the chain widths pretty much converged across brands.