I sincerely doubt you would see a real halfmoon at walmart. Those are show bettas, the kind that go for $20-$60 on the internet. Even if your walmart gets local breeder culs, like is probably how this one gets crowntails, no breeder is going to cull a halfmoon.
That's like a dog breeder getting the perfect puppy and saying "Well, this puppy is absolutely perfect. I could sell him for $500 dollars, or donate him to the Humane Society for someone to adopt. Hmmm, decision decisions..."
I have no idea what a NEW moon is suppoed to be. I haven;t seen it on the IBC website or listed with wny of the breeder sites. I can't even imagine what it would look like. What is a new moon? Possibly something new or possibly some breeder making somehting up to reel in peoplewho have heard half moon and might think that the new moon is something special too.
Anyway, if you see a betta in the store and like him, get him. Don't worry about type or pattern.