Auditing is specifically checking to see if the accounts and/or systems conform to a pre-defined set of specifications (GAAP in this example, but there are all sorts of audits).
Forensic Accounting is investigative. Instead of seeking conformance, you are looking for outliers or specific patterns. Generally I've seen this in support of some sort of legal process. The outcome is less general (an audit report), and is generally useful as evidence in court with regard to certain occurances (where did my cash go; why did this customer get 10% discounts; why am I paying 3x the going rate for sand; etc). Note it is a done-thing to use FA outside of a legal context, so it isn't just constrained there.
Auditing is designed to provide an overall opinion on financial reporting in some form, but limited review for particular issues, particularly "negative" issues, and do not involve detailed specific analyses.
Forensic accounting is much more detailed and focused, particularly to fully understand a specific issue or family of issues, and often used in resolving disputes, including litigation support.
Auditing simply means the opinion of Independent auditors on preparation of financial statements by the management of the company in context of statutory audit and mandatory for public and pvt. companies..
Forensic accounting simply means effective evidences gatther by auditors which "suitable for use in a court of law" and mostly used by govt. agencies.