Zenny is a unit of currency used in multiple games produced by Capcom. The use of the same currency across games does not necessarily mean that the different games take place in the same universe.
The first use was in the Dragonball series of comics, using the spelling Zeni. The creator of Dragonball, Akira Toriyama claims that 100 Zeni is equal to 1 US Dollar.
"Zenni" were some of the first regularly minted bronze coins in the 17th Japanese Tokugawa Shogunate. Modeled after the Chinese "chuen" coin, zenni were round with a square hole in the center.