Privacy is about activity.
Anonymity is about identity.
Security is about ensuring the other two.
I would say:
Privacy is everyone seeing you come and go from a house with no windows.
Anonymity is when you're covered head to toe when you come and go. So nobody know who lives there.
Security is a measure of how good your locks and coveralls are.
Real world examples:
Going to a protest with a mask is anonymous, in public.
Sessions with your court appointed therapist are private, not anonymous.