No, but money changing hands (commerce) impacts whether it is "commercial", and requires a commercial license.
"Impacts", perhaps. But it's not definitive. Especially in California.
For instance: I bought a pickup truck, to use as a tow vehicle for my camper and my wife's boat. Then I discovered that CA requires pickup trucks to be tagged with a (VERY pricey) commercial license, regardless of whether they're used for business. (You CAN petition to tag a particular pickup truck as a personal vehicle - but are then subject to being issued a very pricey ticket if you are ever caught carrying anything in the truck bed - even if it's personal belongings or groceries, and regardless of whether you're being paid to do it. (Since part of the POINT of having a pickup truck is to carry stuff home from the store this would substantially reduce its utility.)
The one upside is that I get to park for short times in loading zones.
If we aren't going to require commercial licenses for commercial driving, then why even have them at all?
And if we ARE going to require them for clearly personal, non-commercial vehicles that happen to be "trucks", why NOT impose this requirement on putatively commercial vehicles that happen to be cars as well?
The real answer to your question is "because the state wants the tax money, and the legislators and bureaucrats will seek it in any way that doesn't threaten their reelection, reappointment, or election to higher office" - in the most jerrymandered state in the Union. The Uber case is one where an appraent public outcry arose, bringing the bureaucrats' actions, and public outcry about them, to the attention of elected officials.
The full form of the so-called "Chinese curse" is: "May you live in interesting times and come to the attention of people in high places."