The dichotomy pointed to with regard to music vs. home theater oriented/labeled subs isn't one to follow with necessity, but rather one that rests with either camp and their potentially self-inflicted limitations. Some if not many of the so-called music oriented subs simply lack the capacity first and foremost to properly handle the demanding low frequency material found in a range of movies on Blu-ray/4K UHD's, while also being restricted into the infrasonic territory. Conversely some Home Theater co-labeled subs may be hellbent on squeezing that last ounce of extension out of a small size factor (albeit typically with larger driver diameter), with all that entails and which may lead them to integrate more poorly with main speakers.
It seems to me though that when overall sub size and driver diameter exceeds that of the more "hifi"-oriented or -accepted sub variants/brands they're automatically relegated into the Home Theater segment (and the associations that follow), which is really a load of B.S. Look at REL: they're small and there seems to be a consensus about their integrating very well with main speakers, hence their popularity in audiophilia. Take then, say, JTR and one of their single or dual 18"-loaded subs of more prodigious size, and mostly there wouldn't be a bloody f*ck of an audiophile who'd give them any serious notice because they're (much) larger, not least the ported variants, and oftentimes more functional looking as well, so naturally they're just about blowing off the roof of one's house, right? Wrong.
What many still don't seem to understand is that with subs you can "have your cake and eat it too," it's just a matter of proper capacity and sufficient* extension from a design that lets size have its say. A well designed and constructed, large and efficient sub will, as always with some groundwork, be able to integrate smoothly with main speakers and accommodate music and movies alike - in both cases even more so than some puny cube of an inefficient sub (unless with a multitude of them). It's not about either/or (i.e.: music or movies), but doing it right from the outset and thereby covering both bases at once.
* A word on "sufficient" extension. This is an area of debate, but first of all infrasonics do make a difference with movies, although for proper effect and those very low frequencies to be truly felt you need prodigious displacement and a lot of power. Some also swear by infrasonic capabilities with music reproduction and its deemed importance here, but subs tuned that low to my ears don't always sound as "alive" in the midbass region. I've found that covering down to an honest 20-25Hz area is plenty deep for most occasions, even with movies, without negative impact on the midbass area, and this way one can also maintain high efficiency without ludicrously sized sub enclosures (i.e.: 20-25 cf. per cab).