Roman citizens were divided into two social classes, Plebeians and Patricians.
The patricians were the upper class. They were the wealthy land owners.
The plebeians were the lower class. They included everyone who was not a patrician. They were sometimes just called plebs. At one time, plebs were the poor people of ancient Rome. They were the workers. Plebeians and patricians rarely mixed socially. (Slaves did not fall into either group.)
In the beginning, their daily life was quite different:
For a while, it was illegal for a pleb and patrician to marry. Under the Republic, that law was finally changed. Still, marriages between the classes was rare.
In the beginning, under the Kingdom and probably under the Republic as well, classes dressed very differently. It was easy to tell who was a pleb and who was a patrician. This site has great pictures to show you the difference. Over time, the way plebs and patricians dressed became more similar. Boys wore a tunic down to their knees. It was white, with a crimson border. Once a boy became a citizen at age 16 or 17, he put aside his childish clothes, and wore an all-white tunic. Roman girls wore a simple tunic with a belt at the waist. When they went outside, girls wore a second tunic that reached their feet.
Both classes were similar in what they could do. All free adult males were citizens, no matter what their class. In both classes, the oldest male was the paterfamilias or head of the family. Old age was honored. If you could afford them, both classes owned slaves. The houses of both classes could be designed the same way unless you were too poor to own your own home. Homes were dependent upon what you could afford. Everyone worshipped the same gods. They observed the same festivals and holy days. Everyone spoke Latin and everyone went to the baths and enjoyed the forum.
Over time, laws changed and styles came and went, but always to the ancient Romans there were two different social levels, even when their daily life was exactly the same - the plebs and the patricians (the nobility.) It was not a question of wealth, although the poor of Rome were mostly plebs and the rich of Rome were mostly patricians. Rather, it was an ancestry or an inheritance of sorts. If both your parents were patricians, you were a patrician. If both your parents were plebs, you were a pleb. When one of your parents was a pleb and the other a patrician, the patricians might accept you into their social circle, but there was always an undercurrent or an awareness that you didn't really fully belong, and the same held true for the plebs.
So even though, over time, the Romans changed many laws to make patricians and plebeians equal under the law, they never really changed their attitudes. You might say they were social snobs, whether they were plebs or patricians.