Folks are getting bound up in shallow semantics in this whole thread and are missing the nuance in your distinctions.
Advertising is part of marketing.
Futhermore, of course marketers will say they control everything (i.e., including advertising). Now let's go ask an advertising agency if they agree. Let's go ask a promotions agency if they agree.
I'm speaking about the process and activities; devoid of typical biz structures and models that manifest those. It's a fool's errand to discuss the latter without first understanding the the basics, the foundation. The fact this thread is off target proves that point precisely.
It's simple. It's called Advertising for a reason. The outputs are called Advertisements for a reason. Whether that's within Marketing's "power grab" or not is not really relevant.