Steam and non-Steam PC are basically different versions of the game which occupy the same slot. You cannot mix-and-match which keys you use. Steam accounts have to use Steam codes, and non-Steam PC accounts have to use non-Steam PC codes.

On a website called CD Keys

That's not an official retailer. It's a grey-market site which means the keys you receive may already be used or may be acquired through fraudulent means. A key that's already been registered is useless as it cannot be registered again.

A key acquired via fraudulent means (usually stolen credit cards) will eventually get banned (usually because the original credit card owner issues a chargeback).