Patricians VS. Plebians

What were the main differences between Roman patricians and plebeians? 

Plebeians were the common folk in Roman times. They were the majority of the population and they were basically everyone, but the rich who were the patricians. They ruled Rome and were the wealthiest of the group. 
What were the Greek versions of patricians and plebeians?

The patricians were called the aristocrats in Greece and the common folk were the non-aristocrats.