The "thinness" of the 9 speed is in the thickness of the side plates.

Recently, I was using a 9 speed chain with cranks from an early 70's 10 speed road bike (2X5).

You CAN NOT use 9 speed chain on a 10 speed cassette or 8 speed chain on a 9 speed cassette because the chain is too wide and doesn't fit between the cogs without rubbing.

You CAN use your 8 speed chain on a 7 speed cassette no problem! You do have to have the chain sized to the proper LENGTH for ANY combination.

http://www.parktool.com/blog/repair-...-length-sizing