Does Apple Watch Cellular clone the SIM card? I have read, that Apple Watch will have the same phone number as iPhone and if iPhone is far away, it can connect to cellular network itself.

Doesn't this mean that Apple Watch clones the SIM and how this corresponds with the statement, that modern GSM network SIMs can't be cloned?
I just checked the SIM ID on my iPhone and paired AppleWatch, and they are different.

I'm not sure why you are assuming that sharing a phone number implies cloning a SIM card. Carriers can design their networks to handle multiple SIM IDs associated with the same account. It's basically the same as two license plates being registered to the same person.