You're right. Each "part" covers something different. Part A (hospitalization) and Part B (medical) are included in Original Medicare, but you can choose to get your Parts A and B coverage through a Medicare Advantage (Part C) plan offered by a private insurance company instead. Part D is prescription drug coverage. You can buy a stand-alone Part D plan from a private insurance company. Or you can get it through a Medicare Advantage plan that includes Part D.
True. If you're enrolled in Original Medicare (Parts A & B), you have the option of getting your Parts A and B through a private company by signing up for a Medicare Advantage (Part C) plan. Often that's smart, because Medicare Advantage plans include your Parts A, B and in many cases your Part D, plus some extras like predictable copayments and deductibles. Remember, you must continue to pay your Part B premium to the federal government.