Sure; every bill has a serial number—but that serial number isn't going to be recorded automatically by every single hand it passes through simply as a matter of how the technology works.
It's not at all far-fetched to imagine a particular bill passing through dozens of hands in multiple states without any unique record of it being recorded anywhere.
A cash card, on the other hand, requires some kind of connection to a central authority to verify what it has on it—otherwise counterfeiting on a grand scale becomes all too easy. So every single transaction at least can be logged, whether or not it is by default—and there's no way for us as regular users of the technology to tell that it's not if the government says it's not. And given that it is a cash card, it will need to be loaded periodically if it is to remain useful—either that, or you'll just have to keep buying new ones with physical cash, which drastically decreases the convenience factor compared to either physical cash or a debit/credit card. It also drastically increases your risk footprint if you are attempting to remain below the radar.
So while anonymity is theoretically possible, untrackability is not—and the moment your identity is associated with even one use of the card (whether by a security camera, or correlation with cell phone location data, or loading it from a debit or credit card, or whatever else), the entire history of that card is at least potentially linkable to you.