VIN stands for Vehicle Identification Number. Every car built within the last few decades has a 17-digit code that indicates the nation of manufacture, model year, basic vehicle type, and individual serial number that sets a particular car apart from all other ones of that make/model/year. The last six digits of my car’s VIN are different from every other 1985 Corolla Sedan.
Your car’s VIN is on your title, registration, and insurance; your plates are only valid if the VIN on the registration matches the VIN of your car, and your title proves that you own that particular car.
Now, since your vehicle color is also on your registration, and since your plates are cross-referenced, if a cop runs my plates and sees that those plates belong on a blue ‘85 Corolla… well, I am safe since my car is actually blue except for the hood. However, if they ran @judochop‘s plates and found that those plates belong on a blue car, the cops will ask questions, possibly arresting him on suspicion of Grand Theft Auto.
The moral is that if you change the overall body color, be sure to update your registration to match. However, if your car is still mostly the color that you wrote on the registration, you will be fine.