Whiz has a few definitions. It’s a verb meaning to move swiftly or to make a sound like an object moving swiftly. As a noun, it usually means one who has remarkable skill in something, and it sometimes denotes a whizzing sound. It’s also a noun in the phrase take a whiz, which means urinate. It’s used in the interjection gee whiz, which expresses amazement or surprise. And there’s whiz-bang, usually an adjective meaning very effective in a novel way.
Whizz is an alternative spelling of whiz in all its definitions. Wiz is an alternative spelling of whiz in the sense one who has remarkable skill in something. Because these spellings came later and have no definitions of their own, they always bear replacement with the longer-established whiz.
On applying the stethoscope, a purring whiz is heard in the situation of the pulsation. [British Medial Journal, Volume 1 (1861)]
Streamlined cars on an overhead railway may whiz across country at 150 miles an hour. [Popular Science (1930)]
During the most recent period under McNamara and his whiz kids, the Pentagon has been led by genius or near genius. [Bulletin of the Atomic Scientists (1967)]
Chess whizz-kid Etienne Bacrot has moved into the history books by becoming the youngest grandmaster. [Independent (1997)]
Alan waddles off to take a whiz and discovers that a real-live tiger—stripes, claws, and all—is lounging in their bathroom. [Planet Weekly (2009)]
The 21-year old fiddling wiz plays the French Quarter Festival today. [NOLA.com (2012)]