They mean the same thing, although the latter sounds slightly more natural.

They're not really interchangeable. Although they theoretically have the same meaning, 'fear' isn't often used to mean 'be afraid of'. It sounds rather formal and old-fashioned when used in this sense. In fact, we tend to use 'fear' to refer to something we are afraid will happen, for example, 'He fears unemployment', or more commonly a phrases such as 'He fears he will lose his job'.

Yes but you use them differently. For example: you could say I'm afraid of heights or I have a fear of spiders.