A siege is a sustained attack. A siege includes direct hostile action against the target. A blockade is a sustained action designed to prevent supplies from reaching a destination. A blockade does not involved direct hostile action against the target. It may involve hostile action against those trying to deliver supplies to the target. The word "blockade" is often used to refer to a naval blockade, where warships will prevent other ships from entering or exiting a port city.

Siege = is the surrounding of a town or fortress with armed forces in order to capture it/force it to surrender. Blockade = the surrounding or closing of a place (perhaps a port) to prevent people or goods getting in or out. You can also have a police blockade - this will stop people crossing a barrier, into say, a government building during a riot.