There is no difference between Balrama and Lord Rama

“The son of Rohiṇī will also be celebrated as Saṅkarṣaṇa because of being sent from the womb of Devakī to the womb of Rohiṇī. He will be called Rāma because of His ability to please all the inhabitants of Gokula, and He will be known as Balabhadra because of His extensive physical strength”. These are some of the reasons why Balarāma is known as Saṅkarṣaṇa, Balarāma or sometimes Rāma. In the mahā-mantra — Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare — people sometimes object when Rāma is accepted as Balarāma. But although devotees of Lord Rāma may object, they should know that there is no difference between Balarāma and Lord Rāma. Here Śrīmad-Bhāgavatam clearly states that Balarāma is also known as Rāma (rāmeti). Therefore, it is not artificial for us to speak of Lord Balarāma as Lord Rāma. Jayadeva Gosvāmī also speaks of three Rāmas: Paraśurāma, Raghupati Rāma and Balarāma. All of them are Rāmas.

Source:A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “Srimad Bhagavatam”, Tenth Canto, Chapter 02 – Text 13