Yet another question designed to confuse me, I think, Henry ;-)
I've just Googled 'anon sim' to check that it doesn't mean something I've never heard of. As the search returned no meaningful results, I assume that 'anon sim' is just an abbreviation for 'anonymous sim'.
An anonymous sim is simply one which hasn't been registered with the service provider. (It's 'anonymous' because there's no record of who's using the phone). If you see a phone advertised with an 'anonymous sim', it means that the current owner hasn't registered their own name and address against the number, so you're free to register your own details with the service provider.
Anonymous sims are detested by the police and security services (who hate the idea of people being able to make untraceable phone calls). They're loved by privacy campaigners, drug-dealers and terrorists.
Chris