If you have a credit card and still pay it off each month, that's still short term debt.

What exactly is the difference between taking cash out of your wallet for each expense in a given month, and keeping the cash in there and taking it all out at once at the end of the month, the exact same amount as the sum of the cash you would have taken out over the month each time you purchase something?

If you're never carrying a balance to the next statement cycle and therefore charged no interest, you're only "in debt" in the most pedantic sense possible, as what you're paying back is not a penny more than what you'd be paying anyway in cash. The literal only difference is when you're paying that same amount.