Damon Knight, an sf author, editor, and critic of fundamental importance to the field, once defined sf as distinguished from fantasy in appealing to the authority of science as justification for its inventions. This doesn’t mean that only hard sf is sf, or other only sf that uses science well is sf. And it very much includes stories that use the trimmings without regard for anything deeper.
In Star Wars, the Force is explicitly mystical. But hyperdrive is entirely technological, as are Death Stars and droids. So Star Wars is a perfect demonstration of science fantasy.
Godzilla is science fiction. The creature has a place in evolution. Atomic power revives it. Its symbolic significance is just that: symbolic. In the world of the story, it’s entirely justified by science. It’s as much science fiction as Primer, Terminator, and Alien, which all appeal to the authority of science in their various ways.
An interesting edge case is Pi. Is the qabbalistic stuff a religious perspective on things that are fundamentally mathematical, or genuinely transcendent? In leaving it open, I’d say Aronofsky is choosing not to appeal to any ultimate authority at all, which puts it in the neighborhood of a lot of weird fiction.