The mechanism for both is the same, which is over-activation of the ryanodine channel on the sarcoplasmic reticulum.
I say that because I know you can use dantrolene to treat both, and dantrolene shuts down the ryanodine channel.
The only "difference" I can think of is that a dopamine-agonist (e.g. bromocriptine) can be used instead of dantrolene to treat minor or nascent cases of neuroleptic malignant syndrome, whereas malignant hyperthermia due to succinylcholine + halothane (or one of the other -fluranes) needs to be treated with strictly dantrolene.