I didn't know what he called it hence my putting it in quotation marks. And MK was originally a Werewolf by Night nemesis, hence his powers being moon related. Since he has reemerged, he hasn't had his powers, making him more Batman like that ever but I'd count his history since the 70's to be more reliable than the past 5 years. Superstrength based on cycles of the moon is one of his powers.
Ahhh... now we're in my territory...
He was originally meant to be the antagonist in a Werewolf By Night two-parter, but by the second part the pair had conquored MK's employers. (It was later ret-conned from being his origin to be the case that MK had long been keeping an eye on their crooked wheelings-and-dealings and infiltrated them to bring them down from the inside).
The recent Huston/Hurwitz years haven't denied him previously having increased strength by the phases of the moon (which was cleverly played for years as possibly being all in Spector's own head or the mystical Khonshu influence - One of the best parts of the series... that it was left open to interpretation). Huston just said that his God had left him and there has never been anything to suggest that this changed back.
Actually I like the last 5 years treatment of MK better than the decades past. Spector/Grant/Lockley/whatever he wants to call himself now don't rely his strength of his "period" moment, but by his erratic tactic and underworld/street knowledge. Yeah now he's more like Batman, but I see him as a more blue collar no-socialite moonlighting stuff wealthy guy in a suit. He doesn't have company (leave that to Stark, Rand, and Taylor of Night Thrasher) but where does he get the money? Probably from financial or mercenary dealings.
Things that differentiate MK from Batman:
- Less emphasis on martial arts, but from tools
- More "Matches Malone" than "Bruce Wayne"
Hurwitz has made him more about tools which, to be honest, I don't particularly like. There's been a few things he's done that I haven't liked, I think he's made Marlene a weaker character as well.
He differs in other key ways as well:
Bruce Wayne's motivation is the symbolic death of his own parents, which have led to his crusade against crime for his own vengeful reasons as well as hoping to prevent the same thing from happening to anyone else.
Spector however is more redemptive, looking to make up for past transgressions in his previous life as a mercenary/soldier of fortune.
One major point that people who speak out against Bats in his own world is "We don't know who's more crazy, the Batman or the people he fights."
Moon Knight takes this to the next level where the reader himself couldn't honestly answer that question, and quite frequently he's CRAZIER than the people he takes down, but still trying to hold tight his moral compass.
That's just a few key ones...