Q. In your follow-up answer to the question about capitalization for Rage Against the Machine, do you mean “eponymous” when you say “self-titled”? Arguably all albums are self-titled.
A. “Eponymous” and “self-titled” are related, but the latter has a specific sense that can apply to something like Rage Against the Machine (the album).
According to Merriam-Webster, something is eponymous when it is named for someone (or something), and that person (or thing) can also be said to be eponymous. For example, Rudolf Diesel was the eponymous inventor of the eponymous diesel engine. And yes, you could also say that Rage Against the Machine is Rage Against the Machine’s eponymous debut album.
But it’s also a self-titled album, which means that a musical group or other entity named (or titled) the album after itself (though someone else may have suggested the idea). So the terms self-titled and eponymous are related but not equivalent. The diesel engine may be named for Rudolf Diesel, but it wasn’t necessarily named by him; it’s eponymous, but it isn’t self-titled. (Besides, engines don’t have titles; they have names.)
If you need more evidence, the term self-titled is in the OED: “Of an album, CD, etc.: having a title that is the same as the performer’s or group’s name” (self-titled, sense 2). One of the quoted examples refers to “the Ramones’ self-titled [debut] album”—which is how we intended the term.
[Editor’s update: Though Merriam-Webster’s definition and accompanying usage note suggest that eponymous can refer to both a named entity and the source of that name, the term has traditionally referred only to the source—as in Rudolf Diesel (an eponym) but not the engine that bears his name. See Garner’s Modern English Usage, 5th ed. (Oxford, 2022), under “eponym; eponymous.” Thank you to our loyal readers for raising this point.]