For example, UC Berkeley offers an astrophysics MAJOR under the title BA degree and also offers a physics MAJOR under a BA degree. Does that mean that these are two different majors with two different degrees?
You are awarded a degree by your college (for undergrad generally a bachelors degree – BA is Bachelor of Arts, BS is Bachelor of science). And for your degree you must declare and complete a major which is the particular area of concentration you took up for your degree.
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So a degree is like an umbrella for specific majors/minors?
Yes. You can get a BA in a host of majors. BA in English. BA in History. BA in Physics, etc…
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A Bachelors is the level you reached and completed. A major is the particular subject matter. I think what’s confusing you is that some science or math topics can be either a BA or BS.
Look at the dept descriptions of different programs and the classes they involve.
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Another way to think of it—your major is the area of study, and so can be at any level. For example, you can get a BA degree with a major in English, and then get an MA degree with a major in English.
In order to be awarded a degree in whatever, a college requires you complete certain courses and/or a number of units. These courses/unit reqs will come from one’s “major” area of study (eg physics), but also come from completing a school’s GE reqs, or from other courses of a student’s choosing. If one satisfactorily completes the requirements of one’s major and any other school reqs (eg GE reqs or completion of a certain number of units), then one is awarded a degree. Your diploma will reflect that your degree is in whatever you majored in.
Astrophysics sounds like one degree and physics sounds D’s like a different one. Look at the requirements for each one. They’re probably different.
For a science subject you usually want to go for the BS rather than the BA, not that employers will be breaking down your door to offer you a job in either case.