Its called The "Katipo spider"
The spider that is black with a white crescent on its back is the Brown House Spider. This spider is often confused with the red-back spider.
A brown spider that has a white diamond on its back is known as a Parson spider. This spider does have a mildly venomous bite.
WHAT KIND OF SPIDER IS A WHITE SPIDER WITH A BRIGHT ORANGE PATTERN ON ITS BACK
My guess is that this spider you saw was either a Jumping Spider (quite possibly a Daring Jumping Spider) or a Parson Spider.
Have seen a very small spider with 4 white dots and 1 red dot. Not a red back. Ta ~Snaff
The worst kind.
Black widow
A spider that has a brick colored heart-shaped marking surrounded by white on its back and lives on the ground might be an orb spider or a white tail spider. This spider might also be a common garden spider found in much of the U.S.
A kind of spider that has a back that looks like a skull with lime green legs and a white back could be a Golden Silk Spider. The skull is clearly marked on a Golden Silk Spider.
a red back.
I just caught a spider that matches this description. After looking online, I think it may be a jumping spider from the family Salticidae. I believe that spider is Phidippus Audax a.k.a the Bold Jumping Spider.
jumping spider family (Salticidae