In everyday usage there is no difference between the terms debt and liability.
Technical usage (jargon) among accountants, however, recognizes a difference. A debt is something that is currently owing under the law. Suppose I have given you a promissory note that says I will pay you $1,000 a year from now. That is a debt which I owe you, even though it is not yet due.
The term liability is broader and includes all debts. All debts are liabilities, but not all liabilities are debts. To take just one example, suppose that a company sells products and gives a one year warranty on them. It cannot be known exactly how many of the products will fail, but one can be reasonably sure that some will. In that sort of situation, accountants will estimate based on the firm's experience how many of the products will fail during the warranty period, and what it will cost to fix or replace them. The sum they come up with will be recognized as a liability for warranty costs. You can see that it does not represent any specific debts. Instead it is an estimate of the amount of debts that will arise during a specific future interval.
By the way, you put this thread in the wrong section which is probably why it took so long for you to receive an answer. You would probably have received a much quicker answer had you posted in Ask a Teacher.
