There’s a clear accounting definiton for a debt or liability. They are synonyms.
If you received something of economic value in the past, and as a consequence are obliged to deliver something of economic value in the future, you have a debt/liability.
OASI - paid for in the past, to be paid in the future, its a debt.
DI - Again, people paid the insurance premiums in the past, so those with a valid claim are owed the money.
SSI - here, if it works like the UK, its not a debt. There’s no insurance premium component.
Salaries? Not a debt. The work is in the future, the salary in the future. Both are in the future so not included.
So my question for you, because from your statement, we clearly have a different definition of debt.
What’s yours?