A safety audit is to promote safety. If a dangerous situation exists a company will have an evaluation to determine where dangerous practices exist. A safe audit is a secure situation. For example, A safe audit is performed behind locked doors where no one can see what is being accomplished. Honestly, this is the first time I have ever seen this topic asked.

Safe is an adjective and it means the audit is safe for usage and it's from a reliable source. The other one "safety" is a noun with a suffix (ty) in the end and it means the audit will be used for the user's safety.

1 doesn't really make sense. A 'safe audit' would be an audit process that is safe. It would be hard to imagine an audit that is not safe. 2 is the correct one. You are referring to auditing the safety of the system.

Thanks a lot.

They are not subtle differences in the general case. They usually have completely different meanings. If you use an adjective, it describes the noun, or in this case, how the noun is performed. If you use two nouns, the first one qualifies the second. It says what sort of noun it is. Again, and to reiterate what I said, a safety audit is an audit of/related to safety. In this example, a security procedure is a procedure about security. Similarly, a safe audit is one that is safe to do. It does not say what sort of audit it is. It could be a financial audit. A secure procedure is a procedure that is secure. Perhaps it can't easily be tampered with, or has measures to check that it is performed correctly. It says nothing about what sort of procedure it is. It could be a procedure for handling money. In this case the similarity of meaning just comes because the security of the procedure _probably_ is related to, overall security.