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Do these mean the same?

She doesn't care if she has to wait for him for an hour or so.
She doesn't care about waiting for him for an hour or so.
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TakaDo these mean the same?
No. They are two different constructions, and it's rare that they can both be used with the same proposition at the end.

She doesn't care if she has to ~ It [doesn't / won't] bother her if she has to
(Also: She doesn't mind if she has to )

She doesn't care about ~ She has no interest in ~ doesn't interest her

She doesn't care/mind if she has to wait. ~ It won't bother her if she has to wait.
He doesn't care/mind if he has to wrap all those packages. ~ It won't bother him if he has to wrap all those packages.
Tom doesn't care/mind if he has to stay home all day. ~ It won't bother Tom if he has to stay home all day.

She doesn't care about playing golf. ~ She has no interest in playing golf. ~ Playing golf doesn't interest her.
He doesn't care about shopping for clothes. ~ He has no interest in shopping for clothes. ~ ...
Susan doesn't care about collecting stamps. ~ Susan has no interest in collecting stamps. ~ ...
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There is also doesn't care for, which is doesn't like.

She doesn't care for watching documentaries. ~ She doesn't like watching documentaries.
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Of these constructions, care about -ing is probably the least elegant. care about is more often better with a plain noun.

She doesn't care about architecture.

And even then, the corresponding sentence with has no interest in sounds better -- in my opinion.

CJ
Comments  
Good. Just as I thought. they are different in meaning.

Thanks, Jim, as always!