There is no such thing as a "Scottish pound" (unless you refer to the pound Scots, which was the currency of Scotland prior to its union with England). The currency of the United Kingdom is called sterling and the banknotes are all denominated in pounds sterling with currency sign GBP.

All banknotes of the pound sterling are issued by banks. By far the largest issuer of banknotes is the Bank of England, which is the central bank of the United Kingdom. It also happens to be the only banknote issuer in England and Wales.

In Scotland, some private banks are permitted to print their own banknotes. These banknotes are fully redeemable at the banks which issued them for Bank of England notes or for coins. This is what "I promise to pay the bearer on demand the sum of £" means. Within Scotland, notes issued by Scottish banks are generally regarded to be interchangeable with those issued by the Bank of England. It is always up to the merchant, anywhere in the UK, whether they wish to accept Scottish issued banknotes, or only Bank of England notes, or no banknotes at all (card payments only).

Many larger shops in England will recognise and accept Scottish banknotes. English banks will generally accept them for deposit. Smaller merchants may not recognise them and refuse them. Again, merchants are never legally obligated to sell you anything in exchange for your banknotes, regardless of who issued them.