I work in TV (on the reality/doc side) so I can offer some information.
“Executive Producer” is one of the vaguest titles there is. Network executives get EP titles–some of them had nothing to do with the show. Others are network executives who DID have something to do with the show in the form of giving notes and overall direction, but didn’t “produce” the show.
Production company executives also get show titles. This varies by company–sometimes all the partners will get an EP credit, sometimes only the ones who actually took an active hand in the show. Typically a production company executive will be involved in getting the show sold (though sometimes a production company is handed a show by a network), and that person will then oversee creative, budget, and network relations, though not usually on an everyday basis.
(Other production company employees may get lesser credits, for example co-producer for the head of development.)
Sometimes EP credits go to someone who essentially got the deal done–they connected an interesting person/persons with the production company. Sometimes a star gets an EP credit–Heidi Klum does for Project Runway, and she does great work as a host, but from what I know I don’t think she has much input into the making of the show. Same for Padma Lakshmi on Top Chef. Specifically on Project Runway, I know there are still listed EPs who haven’t had anything to do with the show in years.
Then there are the people who actually make the shows day in and day out. The title “executive producer” sometimes means the “showrunner”–the person at the apex of the team assembled to make a TV series, reporting to the production company as well as directly to network. But there can be more than one EP on the production team–maybe one in charge of shooting, one in charge of editing, and and even the budget/management person, who would more usually and accurately be called a “line producer.”
And also, showrunners don’t always get EP titles, at least in reality TV. Co-executive producer is still a common title for a showrunner, and I know of one production company that won’t give any showrunner a title higher than supervising producer, which is two rungs down from EP.
My knowledge of comedy and drama is more limited, but I do know of one case where a person who was only directly involved for two episodes of a popular drama series is still getting an EP credit (and getting paid for it) five seasons in. And James L. Brooks, Matt Groening, and Sam Simon have pretty clearly zero involvement with the Simpsons at this point, though they are still credited as EPs.