They're all informal terms for the police. I suppose 'fuzz' is the most informal as it's used in a pejorative way, though I don't hear it much nowadays in BrE. 'Bobbies' is also fairly rare. 'The old bill' is used quite a bit. The 'boys in blue' is something I think you might see more in informal writing- journalism where they didn't want to use a formal term, but didn't want to be rude. It also refers more to the force as a whole than the officers.
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