is a tall cold coffee (based on an espresso or instant coffee) topped with crushed ice – mixed or shaken – accompanied with milk.
is usually understood to be a tall cold coffee (based on an espresso) with ice and a scoop of a vanilla ice cream, cold milk and sometimes also with whipped cream. This varies from place to place and sometimes the ice cream is missing or even is charged for separately, if you insist on it.
While the above two drinks are served in a tall glass, Affogato could be considered a drink which is a dessert. It is a shot of an espresso topped with a scoop of ice cream that slowly melts.