Andy provided a good answer. Care when used as a verb ( an action) can have an s at the end--cares, depending on the subject pronoun. I care, he or she careS, you care, we care, they care. So a person's name would also use the verb CARES. "Maria cares for her baby every day." "Tom cares for his dog when he is sick." When used as a noun, to represent the combined actions of feeding, cleaning, etc, someone or something, then it is just C-A-R-E.

From my knowledge, the word "care" does not have a plural, so the first sentence should read "Birds do not need special care, they can care for themselves." You can use the word "care" in both cases because the context is different and the meaning differs slightly. In the first sentence you are talking about care in terms of feeding and indeed many people do feed birds, particularly over the winter. When the bird is hurt, then it might not be able to look after itself and would need some (medical) care.

The answer depends on the context of the author. Care can refer to "care and feeding," or husbandry of the animal. For instance, the farmer cares for his chickens by providing them with food, water, and shelter. Or it can refer to medical care, specialized attention intended to assist a sick or injured animal.