What a bill of sale actually is
A bill of sale is the seller's receipt: who sold which VIN, to whom, on what day, for what money. It is not a title and it does not register the car.
Is a signed bill of sale the title? No. People fold that sheet and think they own the car. Or they treat it like the registration card. Those are different papers.
A bill of sale is the seller’s receipt for one VIN. Who sold it. Who bought it. The day. The money — or a gift, and the relationship. California prints that on REG 135: identification number, year, make, plate, then sell, transfer, and deliver. Both sides sign. That is the sale record. It is not the ownership sheet.

Florida calls the same job a Notice of Sale and/or Bill of Sale — HSMV 82050. Seller fills the description and the price. If it is a motor vehicle, an odometer block sits on the same page. The footer is the line people skip: this sheet does not move the title. Ownership stays put until the purchaser applies and the office issues a certificate.

That is why the clerk still wants the title. The bill of sale proves the deal. The title is the state’s file for that VIN. Registration is the road permit. A paid price on this sheet does not move the name. It does not put plates on the bumper. It is the receipt you keep, and the receipt a lot of offices ask for when they do move those other papers.
If the header says bill of sale, you are holding the receipt. If it says title, you are holding the ownership sheet. If it says registration, you are holding the permit.