The president can approve the bill and sign it into law or not approve (veto) a bill. If the president chooses to veto a bill, in most cases Congress can vote to override that veto and the bill becomes a law. But, if the president pocket vetoes a bill after Congress has adjourned, the veto cannot be overridden.
The president may not sign a bill with differing values, or if they do, Congress may override their veto. Differing values always end with one party not getting their say/preference.
