Insurers don't determine your actual cash value (ACV) settlement based on what you owe, but rather on what the car is worth just prior to the accident. Let's say you owe $20,000 on your new car, but it's only worth about $16,000. If your car is totaled, you might get a settlement check of $16,000 but still owe an additional $4,000 on your loan or lease.
Let's use the aftermath of a major storm to illustrate the differences between collision and comprehensive. Within that storm, let's consider two hypothetical events: First, a heavy telephone pole was blown down and fell on your truck, or second, you swerved to avoid a falling tree and wound up crashing into a guardrail. In the first event, you couldn't control when or why a tree fell on your car. This kind of accident would get reimbursed under your comprehensive policy. In the second situation, you were driving the car and ultimately swerved into the guardrail. This makes it a collision, and collision insurance pays for the damages.