Woz didn’t create “Apple Basic”. He created the first version of BASIC on the Apple // - Integer Basic. But Microsoft wrote the next version AppleSoft Basic.
Sorry to sperg, but "Integer BASIC" was almost certainly a retronym, a term which didn't exist prior to AppleSoft. Originally it was probably called Apple BASIC, just like ever other [manufacturer] BASIC (at least colloquially).
AppleSoft (MS) BASIC came out very early in Apple II lifecycle, and prior to that there would have been no reason to call the original BASIC anything other than BASIC. Afterwards, of course, all the documentation and commands were updated.