If you held a Scottish pound, you typically held a piece of paper from the bank that you got in return for making a deposit.
From the banks point of view, funds in checking accounts and funds issued as cash were pretty much the same. Just that the cash didn't pay interest, and you didn't know who had it. And it could get lost and never come back to you. (Though perhaps similar to people abandoning accounts sometimes?)
Holding the notes issued by a bank was equivalent to giving the bank a no interest loan. The bank itself invested the funds in loans to other companies. You forewent consumption and took on some risk.
Nominal GDP was remarkably stable over that time in Scotland. In reverse that means that one pound represented about the same share of total economic activity year after year. (The absolute, real amount of economic activity increased a lot.)