What is the difference between an expense and a liability

BIG difference. You are probably confusing them because they are used together in entries a lot. But, first, they don't have to be used together, and second, that doesn't make them the same thing, nor does it make them even related really.

A liability represents something that you owe to someone, or some other obligation (that has value) that you have. All payable accounts represent money that you owe to someone. Accounts payable, notes payable, salaries, payable, etc. An example of a non-payable obligation is like if someone pays you in advance for some work you haven't done yet and you still have an obligation to do the work. (Like if you remodel someone's kitchen and they pay you half up front. You still have an obligation to the remodel job and therefore that's a liability. Called an unearned revenue or deferred revenue on the books.)

An expense is when someone else does a service for you or provides you with something. Like wages expense is for the workers who did work for you, utilities expense for the electric that was provided to you, rent expense for the use of office space, etc. An expense is also when an asset is consumed, used up, drops in value, etc. Like using up supplies or prepaid insurance expiring.

So expenses and liabilities are completely different things. You can record an expense that you incurred but haven't paid for yet, and therefore also have a liability because you still owe for it. But they are two separate accounts representing two different things. They just get used together a lot.

But you can pay an expense immediately with cash and not owe it. And expensing consumed assets doesn't involve a liability. Plus, you can owe for something that was never an expense.