What is the difference between a caregiver and a caretaker?

They are exactly the same thing if you're referring to people. Depending on what part of the world you're in maybe it's called something else.

I think they're the same thing. Unless you are referring to a caretaker for a home, and that would involve taking care of the home and the grounds. Otherwise, when pertaining to caring for a person, a caretaker and a caregiver would be the same thing. Either would be in charge of taking the client to appointments or to run errands, which is what I did when I was employed as a 'caregiver' to the elderly.

Just semantics. When you’re in the midst of it, implication is the last of your issues.