"Insurance" is a really big category, and "full coverage" means nothing unless it's specified in the policy. Not what the agent told you, not what the ad said. I read Supreme Court decisions for 20 years 9-5 M-F that allowed insurance companies to deny claims: the policy didn't cover what happened and the holder didn't know it.
Stolen, burned, or crashed is limited to the value of the car and fairly cheap.
If you hit someone (no upper limit, death starts at $1 million) you're going to need liability coverage - much more expensive.
Medical insurance for injuries you suffer in the car may not be included in either one.