Bachelor's degree
Until the 19th century, a bachelor's degree represented the first degree in a particular faculty, with Arts representing undergraduate study, thus the Bachelor of Civil Law (BCL) at Oxford and the Bachelor of Laws (LLB) at Cambridge, for example, were postgraduate degrees. Vestiges of this system still remain in the ancient universities, with Oxford and Cambridge awarding BAs for undergraduate degrees in both arts and sciences (although both award undergraduate BTh degrees through associated theological colleges, and Oxford awards BFA degrees in addition to the BA) and defining other bachelor's degrees (e.g. BPhil, BCL) as postgraduate awards equivalent to master's degrees, although many postgraduate bachelor's degrees have now been replaced by equivalent master's degrees (e.g. LLM for the LLB at Cambridge and MSc for the BSc at Oxford). The same historical usage of indicating an undergraduate degree by it being in the faculty of arts rather than being a bachelor's degree gives rise to the Oxbridge MA and the Scottish MA).
Professional degree
A professional degree, formerly known in the US as a first professional degree, is a degree that prepares someone to work in a particular profession, often meeting the academic requirements for licensure or accreditation. Professional degrees may be either graduate or undergraduate entry, depending on the profession concerned and the country, and may be classified as bachelor's, master's or doctoral degrees. For a variety of reasons, professional degrees may bear the name of a different level of qualification from their classification in qualifications frameworks, e.g. some UK professional degrees are named bachelor's but are at master's level, while some Australian and Canadian professional degrees have the name "doctor" but are classified as master's or bachelor's degrees.