So in the shop they asked me "what chain do you need" and I said 7. They said "you could try this 6-speed, it is half the price of a 7, and we put it on 7-speeds all the time". I said "ok", only to determine later that my bike is 8-speed. (Excuse: I never use the several highest cogs).
I know "higher-speed" means just that the chain is thinner, fitting the recommended chainring, plus any other with less cogs (because there is more space between the cogs).
And, as expected, my bike now makes all kinds of clicking noises and skips. However, upon inspection, the chain does not rub the chainrings. It fits tight, but does not touch the other chainrings.
I will probably replace the chain for a correct one, but before that I would like to know what is the cause of the problem (the skipping).
EDIT: some more detail
We are talking a $300, used regularly for three years. Of it, only the chain has been replaced - twice.
If needed, I will post a photo tonight. Just ask in the comments!