

By that logic bank notes are not cash, only coins are cash.
Look at a bank note and read what it says: " I promise to pay the bearer on demand the sum of five/ten/twenty/fifty pounds" the the signature of the governer of the Bank of England (or whichever Scottish bank issued it). They’re literally promissory notes in lieu of cash.
No, they’re notes. What I’m saying is your logic applies equally to bank notes as it does to cheques.