The Ancient Greeks developed many of the building styles that we still use today. Features like decorations at the top of columns had been invented by earlier civilisations, such as the Ancient Egyptians, but they used designs such as lotus leaves.
The Ancient Greeks developed their own styles, and it is these that have been used down the ages. There are three main styles, Doric, Ionian and Corinthian. Each was developed in a different place, so, for example, the leafy column tops were developed in the city of Corinth, hence Corinthian.
As it happens, the Greeks hardly used the Corinthian design at all. It was the Ancient Romans who took a fancy to it, and that is why we find it in many Roman, rather than Greek buildings.