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Great question!
The simplest answer:
Anxiety is standing in one's slaughter line. Fear is seeing the man with the hammer.
The more clinical answer:
Fear has an object; anxiety does not. Anxiety is fear of the unknown.
Now, ask me about obsession. :-D
Fear is a real feeling and can be released, anxiety is avoidance of real feelings and prefers to panic...panic is the deliberate avoidance of terror. It's a no no no denial of feeling and cannot be released, it's stored.