No, vehicle registration and car insurance are not the same thing, but they are related. Showing proof of insurance that meets your state's minimum requirements is part of the BMV or DMV vehicle registration process. Additional steps include providing proof of ownership (car title), passing a vehicle inspection, and paying any fees. Most state motor vehicle departments accept an insurance card, a printed coverage statement and, depending on the state you are in, an electronic coverage statement as proof of insurance.
Contact your insurance company and they will send you all the documents you need to prove that you have insurance. Keep in mind that you could lose your e-discount if you choose to receive your car insurance card in the mail. However, drivers who choose not to purchase auto insurance must show that they have sufficient funds to meet the state's financial responsibility requirements (PDF) in the event that they cause an accident. Most states require minimum auto insurance and vehicle registration coverage, so it's important to have proof of insurance and registration when driving.
Whether you're buying a used car from a private individual, a new car from a dealership, or paying a loan for a vehicle you've been driving, you'll want to make sure you get the title to the vehicle to prove that you're the full owner. If you're buying a used car, you'll need at least the minimum car insurance coverage required by your state before you can legally get behind the wheel. You must inform your insurance company that you have purchased a used car and that you want to add it to your policy. This information is not an insurance policy, does not refer to any specific insurance policy, and does not modify any provision, limitation, or exclusion that is expressly stated in any insurance policy.
You may be able to buy a used car without having an insurance policy, if you buy a car from a private seller, but you won't be able to legally drive the vehicle without car insurance. In many cases, it can be cheaper to insure a used car than a new one, especially if you have full car insurance or auto collision coverage. The registration rules for vintage or classic cars may differ slightly from those for traditional vehicles, but they will likely still require insurance. That said, many insurance companies offer policies for vintage or classic cars that meet your state's old vehicle registration requirements and also provide protection for your classic vehicle.
With most insurance companies, you'll be able to get proof of car insurance immediately after buying a policy.