It often depends on context. For example, to fear and to be afraid could mean exactly the same thing, e.g. I have a fear of flying / I am afraid of flying. However, in another context, they could mean something different: "I fear I am running late," does not actually mean the person is afraid, it's more a turn of phrase (in this case, a posh way of saying you're late!)
I would say dread is something a bit different - a sense of foreboding. Imagine having a deep-seated fear or distaste for something that you expect is actually going to happen. You might dread going to the dentist, or dread Mondays ;) It sits inside of you for a long period of time. In contrast, fear is something that suddenly happens in response to something else.
To scare would be an action taken - I can scare my cat if I make a loud noise. Then again, scared and afraid are synonyms, so I can be scared of the dentist and afraid of the dentist. There is no difference.