The five orders of architecture: Tuscan, Doric, Ionic, Corinthian and Composite. The second, third and fourth are the Greek orders. The Romans added the first and last order which are modifications of the Greek orders.
The Corinthian order is similar in design to the Ionic. The capital is the most distinct difference. The accompanying image does a good job of displaying the very decorative components that set the Corinthian order apart.