Doctors normally call this the celiac plexus.(that is the US-E spelling) The term solar plexus is a lay term, not a technical one, but it is not used in the ways you suggest. Gut or belly would be where you get punched. People speak of having a gut-feeling, but not of being frustrated there; frustration is not usually anatomically located.
In the context of televised sports, particularly American football, you'll occasionally hear the announcers say that a player "took a shot to the solar plexus" and "had the wind knocked out of him." That's the only context in which I've heard the term as a non-medical person.
In my experience the solar plexus is the set of muscles directly below the rib cage. The gut or stomach is right behind the belly button, below the solar plexus. You really have to have a context to identify the term, in many cases.