ive written both, and i think ive found the defining line between them.

both horror and action use gratuitous violence. however, the power level of your protagonist determines which genre it is.

a powerless protagonist makes it horror. a powerful protagonist makes it action.

lets use a nfh example:

nfh has a lot of action. surely youre not frightened by umbra fighting asher hand to hand in arc 3. theyre on equal terms- its a fight, clear and simple.
compare that to arc 8, where umbra is made powerless and tortured and harassed by asher. thats a little scarier, right? hes completely defenseless. its not a fight anymore.

ditto for when victor is put in danger. hes inherently more "helpless"

which scene makes you more frightened: a chasing down a scared little girl, or a little girl fighting a monster with her magical powers?

horror protagonists are more likely to be everyday people like you and me. which means theyre less likely to be able to fight the monster terrorizing them.

if you want even more terror, increase the power of your villain. the imbalance here is key. thats why an adult brutalizing a child feels worse than an adult brutalizing another adult. eventually, youll end up in some lovecraftian cosmic horror territory  (lik world eater)

no matter how much bloody violence you show me in an action flick, its probably not gonna be scary. but chalking your protag down a few levels makes it scary

so, yeah, thats the difference for me. thats what makes violence scary.