I found that the Science Fiction & Fantasy site indeed allows such questions.
What is the difference between the topics of these two sites that caused these different decisions?
Or is it just that the decision makers of the two site have different views of the same thing?
Science Fiction & Fantasy mod here, and also highish-rep Movies & TV user and meta contributor.
A bit of both.
The "decision makers" (active community members including moderators and others posting on meta) at Science Fiction & Fantasy have generally been in favour of allowing story-ID questions, since the site's genesis back in 2011, and even attempts to impose stricter quality control on them has generally been poorly received. They've always worked well enough at Science Fiction & Fantasy: of course with some bad ones that need to be closed, but we've never felt flooded by waves of low-quality ID questions.
By contrast, Movies & TV "decision makers" (to use your phrase - again meaning moderators and other active meta contributors) were largely against ID questions for years, even when site policy allowed them. They were allowed at least since 2012, but problems with quality control of these questions was discussed repeatedly on meta. A 2016 discussion Shall we ban identification questions? resulted in a resounding decision against banning them, but with far more votes than active meta users - the first few votes were in favour of banning them, but then more casual users arrived at the featured meta post to cast their votes, and the decision went pro-ID. Then in 2017, another meta post Check in on Identification questions, featured for a month in December (when SE activity is usually less as many people are busy having holidays IRL) and "not intended as an outright vote to keep or ban such questions", received an answer which, during that period (in which no fully pro-ID answers were posted), gathered enough votes to count as a consensus for We are discontinuing support for identification questions in early 2018. Then the purge started, with thousands of questions deleted and a massive rep loss for the active ID answerers. (When the wider community, beyond just the site fanatics and active meta users, became aware of the decision to ban ID, the votes rapidly turned around, so that now the "consensus" on the original "Check in" post is solidly pro-ID and the ban announcement is the most unpopular post ever while the most popular are pro-ID, but by then the ban was already a fait accompli.)
That addresses how it came about that ID questions are banned here but not on Science Fiction & Fantasy, in terms of the people and decisions involved. The why is a little harder to quantify, but I can testify that question quality for ID was always significantly lower here. Of course there were many good, detailed and well-asked, questions, but they were drowned by a huge number of short low-effort posts. My personal view, supported by anecdotal experience and weakly by per-tag data on Science Fiction and Fantasy, is that book ID question naturally tend to be better than film ID questions. Perhaps people retain memories better from reading a book, or it's easier to casually catch just part of a film whereas a book tends to be read cover-to-cover.
TL;DR: there is some philosophical disagreement between the two sites' decision makers about the value of ID questions in general, but it's also a fact that this site always struggled more with drowning in low-quality ID than Science Fiction & Fantasy ever has.
