Yes, that is the difference. The Bereans looked for the authority of the apostle and the authority of Scriptures to agree. Paul was the new authority, after all. And he was specifically appealing to the Old Testament Scriptures, so the Bereans, being faithful, looked to the Jewish scriptures to verify what Paul was saying. And when they verified that Jesus indeed fulfilled the prophecies of the Christ, they believed. At all times during this story they remained under the authority of the Church and the pre-Church - first as Jews and then as Christians.
*"they came to Thessalonica, where there was a Jewish synagogue. 2As his custom was, Paul went into the synagogue, and on three Sabbath days he reasoned with them from the Scriptures, 3explaining and proving that the Christ[a] had to suffer and rise from the dead. "This Jesus I am proclaiming to you is the Christ," he said. "
Then later in the chapter Paul preaches the same way to the Bereans:
"the brothers sent Paul and Silas away to Berea. On arriving there, they went to the Jewish synagogue. 11Now the Bereans were of more noble character than the Thessalonians, for they received the message with great eagerness and examined the Scriptures every day to see if what Paul said was true. "*