The plebeians (the commoners, both rich and poor) fought only one order: the patricians (the aristocracy). They did not right for rights. All Roman citizens had the same rights. The poor plebeians fought for their economic grievances. The rich plebeians fought for access to the offices of state and the seats of the senate (which the patricians monopolised) and power sharing with the patricians.
There is not a four letter word for the patricians. The patricians called themselves patres (fathers). This is what the term patricians is derived from. The singular of patres is pater. Neither of them is a four letter word.
The term plebeian is English. The Latin term is plebs (plural plebem). Therefore, there was a four letter word the plebeians, not the patricians.
The war between the patricians and the plebeians was/is called "the Conflict of the Orders"
Social classes in Rome were called orders. The patricians were the aristocracy. The plebeians were the commoners (all non-patricians, both rich and poor). In the Early Republic, the plebeians fought the patricians in the 200-year conflict of the Orders. The poor plebeians fought for their economic grievances. The rich plebeians, who led the plebeian movement, also fought for power sharing with the patricians, who monopolised it. Eventually, the rich plebeians obtained power sharing and were co-opted into a patrician-plebeian oligarchy. These rich plebeians were given equite (cavalryman) status. The equites were the second highest ranking order in Roman society. At this point the rich plebeians turned the back on the poor, whose economic issues were never addressed properly and remained plebeians.
friction between the patricians and the plebeians
The Romans did not protest for equal rights. All Roman citizens had equal rights. From 494 B.C. to 287 B.C. there was the Conflict of the Orders between patricians (the aristocrats) and plebeians (the commoners). The poor plebeians protested about their economic grievances: the abuse of defaulting debtors by creditors, the interest rates of credit and shortages of land for the poor to farm. The rich plebeians fought for power sharing with the patricians, who in the Early Roman Republic monopolised the consulship (the consuls wee the two annually elected heads of the republic) and the seats of the senate.
The plebeians (the commoners) fought the Conflict of the Orders ( 494 BCE to 287 BCE) to gain power-sharing with the Patricians (the aristocracy)
friction between the patricians and the plebeians
The main struggle of the orders' central conflict was war.
The senators were members of the aristocracy and the wealthy entrepreneurial elites. Therefore, they were treated with the respect due to the top layers of society. There were, however, times of conflict with the senators. One of these was by rich plebeians during the Conflict of the Orders (between patricians and plebeians) of the early Republic in which the rich plebeians fought to gain access to the senate and the consulship (the office of heads of the Republic) which were monopolised by the patrician aristocracy. They eventually succeeded in gaining power-sharing Poor plebeians were often in conflict with the senators through most of the republican period. Poor plebeians often fought for reforms which would relieve the poor and which were opposed by the senators. After the Republic these was at times conflict between the emperor and the senator.
The patricians (aristocrats) and plebeians(Commoners) had the same rights. Every Roman was equal before Roman law and all Roman citizens had the seem rights. In the Early Republic the patricians monopolised political power. The rich plebeians fought to obtain power-sharing and succeed in the conflict of the orders of the Early Republic.
The conflict of the orders between patricians and plebeians
The plebeians were the commoners. In the early republic the concern of the rich plebeians was to attain power-sharing with the patricians (the aristocrats) who monopolised political power . They achieved this in the 20-year Conflict of the Orders between patricians and plebeians. The concerns of the poor plebeians were economic: indebtedness, the interest rates of loans and shortages of land for poor farmers.
The Conflict of the Orders, the 200-year struggle between patricians and plebeians, was over before Rome developed an empire.