For vehicles purchased from in-state dealerships, sales tax or the Infrastructure Maintenance Fee (IMF) is collected at the time of purchase. The dealer can also arrange for the South Carolina Department of Motor Vehicles (DMV) to mail you a new license plate, decal, and registration that are good until next year.
The bill you received is for the personal property taxes due on the vehicle. This is to cover the plate and registration that was mailed to you in advance of this bill, which is separate from sales tax or IMF. Personal property taxes are to be paid within 120 days after the purchase of a vehicle from a dealership. The dealership would have provided you paperwork that you signed, acknowledging that the property taxes would be due in 120 days.
The most commonly provided form by South Carolina dealerships is the Affidavit & Notification of Sale of Motor Vehicle, which notes property taxes as being due in 120 days in the "Property Tax Section" at the bottom-right of the page. The documentation and wording may vary depending on the dealership.
Sample: