Disclaimer: The following units are semester credit, semester hour, semester unit, trimester credit, trimester hour, trimester unit, any other name for the standard unit of higher education. They are not quarter credit, quarter hour, or quarter unit by quarter systems.
Originally, there is no distinction between Bachelor of Arts and Bachelor of Science, but today, different institution defines the standards differently. From the least rigorous standards, we have
Bachelor of Arts - at least 24 units in major, at least 12 upper division units
Bachelor of Science - at least 36 units in major, at least 18 upper division units
to the most rigorous standards, we have
Bachelor of Arts - at least 24 upper division units in major, one year foreign language
Bachelor of Science - at least 36 upper division units in major
Not necessary more course requirement, but a shift to upper division courses, but that usually means that lower division prerequisites don't count towards determining Arts or Science degrees.
The abbreviations of the degrees are as follows:
Artium Baccalaureus (AB) = Bachelor of Arts (BA)
Scientiae Baccalaureus (SB) = Bachelor of Science (BS)
Philosophiae Baccalaureus(PhB) = Bachelor of Philosophy (BPhil)
Artium Magister (AM) = Master of Arts (MA)
Scientiae Magister (SM) = Master of Science (MS)
Philosophiae Magister (PhM) = Master of Philosophy (MPhil)
Artium Doctor (AD) = Doctor of Arts (DA)
Scientiae Doctor (SD) = Doctor of Science (DS)
Philosophiae Doctor (PhD) = Doctor of Philosophy (DPhil)
The Latin form of abbreviation are used by the Cambridge style, while the English form of abbreviation are used by the Oxford style. Note that in the UK science is "Sc," while American Science is "S" such as Master of Science (MSc) for UK. Also, the Science degree is an inventions of Cambridge to be different from Oxford. Otherwise, the typical degree is Bachelor of Arts or Bachelor of Philosophy depending on the lower (general) faculty. That's why traditional institution will offer Bachelor of Arts degree even in hard science and engineering majors.
The lower (general) and upper faculties: In the middle ages, higher education divides into general faculty and the upper faculties. The general faculty is known as the Faculty of Arts (or Faculty of Philosophy) while the upper faculties are the Faculty of Medicine, Faculty of Law, and Faculty of Theology. In such tradition, completing a degree (Bachelor of Arts or Bachelor of Philosophy) in the lower faculty is the minimum prerequisite to enter the higher faculty. However, there are times where completing the second degree (Master of Arts or Master of Philosophy) is necessary to enter the higher faculty. Usually, the first degree is 4 years or study, and the second degree is 3 years of study (or 2 years teaching). The higher faculty has a first degree (Bachelor's degree) and second degree (Doctorate). The designation of a Doctorate degree is to distinguish between the higher faculty from the lower faculty even though Master and Doctor are equivalent terms during the middle ages.
The Basic, Lower, or General Faculty known as either the Faculty of Arts (Most of Europe)
or the Faculty of Philosophy (German and few others) has changed around the 19th century. The
old Bachelor of Arts gets renamed into the modern High School diploma,
while the old Master of Arts become the modern Bachelor of Arts. As follows, modern Master of Arts requires more advanced knowledge than the old way.
And then, we have the Doctor of Philosophy instead of the Doctor of Arts as the highest degree because the German's higher education was more advanced than the rest of Europe for significant duration of the 19th Century. At first, the Doctor of Philosophy is the German's version of the Master of Arts degree, but its reputation grew and this degree becomes more prestigious.