The Corinthian column and the Corinthian Order were created in ancient Greece. Ancient Greek and Roman architecture is collectively called Classical, and, so, Corinthian columns are found in Classical architecture.
A Roman Doric column is similar to Greek, with two exceptions: (1) Roman Doric columns often have a base on the bottom of the shaft, and (2) are usually taller than their Greek counterparts, even if the shaft diameters are the same.
Examples of Buildings with Ionic Columns: Western architecture is filled with examples of Ionic columns. The Colosseum in Rome (80 AD) was built with Doric columns on the first level, Ionic columns on the second level, and Corinthian columns on the third level.