Which one of the following is recommended to be used, and what is the difference between both of them?
You do not have to worry about anything.
You do not have to be worried about anything.
The first phrase has an active infinitive, and the second is a passive infinitive. They have virtually no differences in meaning (the one slight difference being that the first one implies that you do not have to do something, while the latter implies that you do not have to have something done to you), and they are completely interchangeable.
They're both perfectly acceptable and there's no difference in meaning between the two.
To answer the question in the title, not just the sample sentences in the question, I would suggest:
... if you want to talk about a general, long-lasting worry, say I worry about you, and if you want to talk about a specific worry related to a specific event that’s happening now (or happened recently), you can say I'm worried about you.
from bbc learning english.