As you are likely aware California does not offer a grace period after your vehicle's registration expiration date. If you do not pay your renewal fees on or before the date of expiration shown on your current registration card or penalties will be due in accordance with Vehicle Code Sections 9552 - 9554. The longer you delay payment of fees, the greater the penalty amount will be.
The California Department of Motor Vehicles website has a chart of the registration fee penalties for renewing your registration late or you can call 1-800-777-0133 to find out what your fees are. The chart shows that penalties range from 10% of the normal fees up to 160%, the longer your wait to renew the higher the fees.
The vehicle code states that besides the imposition of monetary fines or fees as specified in the VC, delinquent registration may result in impoundment of the vehicle. So it would appear that besides fines your car could be impounded if you are found driving with expired tags. From what we have read many times it is up to the officer to decide if they will write a ticket and impound the car or give you a minor "fix-it" ticket.
If you get a fix-it ticket for expired registration normally you can get the ticket dismissed if you correct the situation by renewing your registration. If you get a fix-it ticket then administration fees might also still be required. But if your registration has been expired for quite some time, then likely you would receive a violation ticket instead of a fix-it ticket.