Don't worry.
I have Campy shifters and rear der and rear cassette, Shimano front der and chainrings, and Sachs chain.
What they are talking about with the chain sizes is the width, which varies depending on the number of cogs in your cassette. More cogs = narrower chain. (gotta fit it all onto the bike somehow!)
Just make sure you are using a "9 speed" chain with a cassette with 9 cogs, 8 with 8, 10 with 10, etc, and you should be fine!
Are you having any problems?
If it's all working, don't fret. If you are having wear issues or shifting problems take the bike in and find out if all the drivetrain components are meant for the same number of rear cogs. (even the front der and chainrings will vary depending on the number of rear cogs)
Chainrings, ders, chain, and cogs need to match. Brands not so much.
(learned at the enlightened feet of Chris at Robinson Wheelworks in San Leandro CA, one of my bike mechanics gurus)
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson