Both "taze" and "tase" are words originating from "Taser," which is a brand name of a specific electroshock weapon. The inventor of this weapon, Jack Cover, named it "TASER," an acronym for "Thomas A. Swift's Electric Rifle." In terms of meaning, both "taze" and "tase" are slang terms that have come to be used to describe the action of using a Taser weapon on someone.
The difference essentially comes down to the spelling preference and regional usage:
Ultimately both words express the same concept and are understood in the same way. In some circles, these words could also be considered "verbing," where a noun (in this case, a brand name) is used as a verb.
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