What's the difference between "Don't worry" and "Don't care"?

[Robert]

Test No. incompl/elem-25 "On my Mobile", question 9

Don't ......... - I'll see you very soon.

(a) concern
(b) care
(c) worry
(d) mind

Test No. incompl/elem-25 "On my Mobile", answer 9

Don't worry - I'll see you very soon.

Correct answer: (c) worry

Your answer was: incorrect
Don't care - I'll see you very soon.
_________________________

Why care isn't correct?

[Torsten]

Robert, please take a look at the context you and you will find an answer to your question. If not, let us know.

Don't worry - it'll be alright. (positive)
I don't care what you say - I know I'm right. (negative)

TOEIC listening, talks: Afternoon traffic report sponsored by fitness studio