liability
Definition
An obligation that legally binds an individual or company to settle a debt. When one is liable for a debt, they are responsible for paying the debt or settling a wrongful act they may have committed. For example, if John hits Jane's car, John is liable for the damages to Jane's vehicle because John is responsible for the damages. In the case of a company, a liability is recorded on the balance sheet and can include accounts payable, taxes, wages, accrued expenses, and deferred revenues. Current liabilities are debts payable within one year, while long-term liabilities are debts payable over a longer period.
revenue
Definition 1
For a company, this is the total amount of money received by the company for goods sold or services provided during a certain time period. It also includes all net sales, exchange of assets; interest and any other increase in owner's equity and is calculated before any expenses are subtracted. Net income can be calculated by subtracting expenses from revenue. In terms of reporting revenue in a company's financial statements, different companies consider revenue to be received, or "recognized", different ways. For example, revenue could be recognized when a deal is signed, when the money is received, when the services are provided, or at other times. There are rules specifying when revenue should be recognized in different situations for companies using different accounting methods, such as cash basis and accrual basis.
Definition 2
For the government, the increase in assets of governmental funds that do not increase liability or recovery of expenditure. This revenue is obtained from taxes, licenses and fees.
Maybe it is hard to tell the difference because often when you purchase something you also create a libility by buying that asset on credit and you are confusing the acquiring of an asset with revenue. Also, when someone "pays" for your goods or service by giving you something other than cash like with what happens through bartering.
For example, you need a new copier machine for your office and you are a plumber. A friend has a business and they are buying a new one and offers to "sell" you theirs if you agree to replumb their bathroom which has some leaky pipes. You agree and the copier becomes yours, but you can't do the work for a few days. This copier is now an asset of your business and you have an obligation to make good on the agreement and do the plumbing work. However, the value of the copier is considered revenue, because it was received as payment for services. This kind of situation can get tricky when recording it in the books.
Hope this helps clarify things for you.