After making it through a fairly extensive interview process with this company, including multiple on-site interviews and homework-like assignments, today I received an email informing me that they would be pursuing other candidates. However, this email referred to a position that was not the one I had originally applied to, and that had never been mentioned before in any of my communications with this company, so I'm unsure what to make of this and how I should proceed.
More specifically, the email says something along the lines of, "Thank you for taking the time to meet with us and interview for position X." However, I applied to position Y, all other emails I've received from this company refer only to position Y, and I never heard anything indicating that I was being considered for any position other than position Y. One of the people I interviewed with did mention that they were also in the process of interviewing candidates for a role that it seems very likely was position X, but it felt much more like they were telling me this to give me more information about the team I'd be working with in position Y, rather than because they wanted to consider me for position X instead of/as well as position Y. Furthermore, I checked the company's job listings again and position X is now listed, but it requires multiple years of experience (which, as a recent college graduate, I don't have), while position Y was entry-level.
It seems like the most plausible explanation for this is that they simply plugged the wrong job title into their rejection email template, and so I don't want to come off as bitter by sending a response email that essentially just points out a typo. At the same time however, although I'm sure I'm probably just grasping at straws here, I'd still like to hold out hope that maybe they really did mix up which position I was being considered for, and so pointing this out to them could still possibly lead to me being given a job offer.
So, should I even bother responding to ask for clarification, and if so, how should I go about phrasing my response so as to limit the chances of it coming off as bitter and/or desperate?