Or any way to distinguish this?
I agree with what the others said. Another characteristic that makes them unique IMO is the following:
When I bought the on-chain stamp, I requested for delivery of the physical stamp. When I received the physical stamp and compared it to other off-chain physical stamps, it was exactly the same.
However, the uniqueness here, is that I had a physical stamp, unscratched (in mint condition) were at the same time, the digital stamp token (corresponding to that physical stamp) was already in my ETH addy. When you purchase from the on-chain store, you receive the digital stamp to your ETH addy.
This is pretty unique (and not quite sure if it is a correct implementation/designing way), since I have in my possession an unscratched/unredeemed physical stamp, with an already redeemed digital token.
To be honest, I was expecting to receive a scratched physical stamp. I have 2 of those physical on-chain unscathed stamps, hence this shouldn't be coincident.
Edit: So to answer the question "any way to distinguish this": If you have a physical stamp, by checking the 6 digit code, you can easily distinguish if it is an on-chain or off-chain stamp. (at the on-chain stamp you will see the tx that the digital stamp was "moved")