I don't know where you learned or who tought you but you're way off base.
1st, where most internal audits and internal audit programs go wrong is that they never get past asking people if they have a procedure and if they know the policy. This happens because many of the folks charged with the responsibility to establish so called internal audit programs and conduct audits don't know $hit-from-shinloa about what they are doing and/or the reason why. This starts with thinking that all we need is an auditor training class and ends at the failure to develop a sound competency process.
2nd, regardless of the type of audit be they internal, external, or whatever the purpose of every management system audit is exactly the same and that's to
verify conformance...just look in 9001, 14001, 13485, 9100, 18001, 16949, 22000, or whatever and you'll see it very clearly written and never paid any attention to.
Do you really think that I, a 3rd party auditor, look at special stuff for 3rd party auditors only? I look at the same stuff, I interview the same people, I observe the same activities as the internal guys, unless of course the internal guys are just going through the motions, following some bogus, bull$4it, pre-printed checklist that is used time and time again with no deviation or change from audit to tired useless and wasted time audit.
There are hundreds of books published by "audit guru's" and "experts" and "I know more than you, blah, blah, blah's" about how to do internal audits and how to set up programs and all that other horsehockey

that contain no more real substance than good old,
in need of revision ISO 19011 when all of the fluff is removed and it provides guidance for to begin with.
The weakness and failure rests with a poorly planned process (and most don't know the process approach to establishing audit programs, planning for and conducting audits, developing and evaluating auditor competence, monitoring and measuring the program and seeking improvement).