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Why were the titles master, doctor, and professor once nearly equivalent?

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Gothic-style stone buildings of Corpus Christi College, University of Cambridge, surround a large green courtyard in Cambridge, England. — University Corpus Christi College, University of Cambridge, England.

In the context of medieval university structures, the titles of master, doctor, and professor were once nearly equivalent because they all signified the same professional status: admission into the teachers’ guild with a formal license to teach.12

During the 13th century, universities functioned as guilds where degrees served as professional certifications. A master or doctor was a scholar who had completed their studies and passed examinations, granting them the authority to instruct others. While these terms were initially interchangeable, usage varied by region and faculty:23

Regional Differences: At the University of Paris, the title "master" was more common, while the "doctor" title was prevalent in Italian universities like Bologna.12
Faculty Distinctions: In many institutions, scholars in arts or grammar were typically called masters, whereas those in higher faculties—such as theology, medicine, and law—were titled doctors.2

Over time, the doctorate became increasingly esteemed as a higher title, eventually becoming the standard for advanced degrees globally, while the term professor evolved to describe the role of the teacher within these academic guilds.12