Wikipedia isn't a source of facts, but if you read your own link, you will learn that open carry used to be permitted, but since 2012 open carry of all firearms, loaded or unloaded, is prohibited.

"No license or permit is required to openly carry a loaded firearm in unincorporated areas where discharge is not prohibited by local ordinance."

...Maybe every county has adopted local ordinances prohibiting open carry in unincorporated areas?

"Prior to January 1, 2012, it was legal to openly carry an unloaded handgun in public. In October 2011, Governor Jerry Brown signed a bill that modifies the law on openly carrying an unloaded firearm to match the restrictions for openly carrying a loaded weapon.[63] Legislation was later signed by Governor Brown to expand these restrictions to long guns and shotguns, except while hunting."

This seems to be making the law for unloaded carry the same for loaded carry, and doesn't address the legality of loaded carry.