Here’s the definition of “titular.”
Here’s the one for “eponymous.”
Note that initially, “titular” has nearly nothing to do with the title of a book or story or what have you. It has to do with a title, as in an office (like queen or king or president), and with that title being “in name only” with no actual power.
“Eponymous,” though, has everything to do with appearing in the title of a work. Think Jane Eyre. She’s the main character, and her name is the title of the book.
Over time, people have gotten confused and begun to use “titular” in a similar manner as “eponymous.” Now, we can draw a line between them on that front as well. In Kipling’s “The Man Who Would Be King,” Dravot is the titular character. He’s the one who comes up with the scam that costs him his life and lands Carnehan in an asylum. His name doesn’t appear in the title, but he’s the one referenced in it.
It’s another case of language change, and another thing that peevers peeve about. Keep in mind that unless the title is a name (Oliver Twist, Eleanor Rigby), “eponymous” isn’t the right choice.
Grammargeddon! 
I was searching the web for a clear distinction between titular and eponymous and I appreciate the explanation you have provided. I have a follow-up question: is it eponymous, titular, or neither if a name is directly stated in the title, but there are other words as well? To use Keanu Reeves movies as examples:
John Wick; Constantine; Keanu: In each of these, Keanu’s character is eponymous. The movie is named after the character.
The Devil’s Advocate; The Watcher: In each of these, Keanu’s character is titular. The movie references his character but does not name him.
Bill & Ted’s Excellent Adventure: Keanu plays the character Ted Theodore Logan. His name is directly listed in the title, but the film is not named after (only) him. Is Ted titular? Eponymous? Neither? Titular feels more accurate, but it’s not exactly the same as the examples you provided. The movie is specifically referring to the adventure itself, not to the characters. Also, can you have two or more titular characters?
To sadly depart from Keanu examples, what about the cartoon Bob’s Burgers? Bob is a character, but the show is named after the restaurant, just like Bill & Ted’s Excellent Adventure is actually referencing an adventure. But the restaurant is a tangible thing after which something can be named, unlike an (unnamed) adventure. My understanding is that the restaurant is eponymous. Is the character Bob . . . anything? He’s clearly not eponymous if you strictly apply the definition above, but is he even titular? Could there be a titular character who owns an eponymous restaurant? Or is he merely the “namesake purveyor,” perhaps?
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you’d say the ‘the titular restaurant is at the end of the road….’ or ‘as he bit into one of the titular burgers, he…’
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SO what about “The Terminator”? The Terminator LOOKED human but was an inanimate machine and didn’t have a name. So would The Terminator CHARACTER be eponymous or titular? Foe that matter what if the title refers to an inanimate object that’s in the film. If a movie were called “The Matrix” (going back to Keanu Reeves again) would the Matrix environment in the movie be eponymous or titular?
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