Let's use the aftermath of Superstorm Sandy as an example to illustrate the differences between collision and comprehensive. Within that storm, let's consider two events that might have happened: 1) a heavy tree branch fell on your car, or 2) you swerved to avoid a falling tree branch and wound up crashing into a tree. In the first event, you had no control over when or why a tree branch would fall 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 tree, which makes it a collision, and collision insurance therefore pays for the damages. Events like the hypothetical ones stated above are why it's important to differentiate between the two types of coverage.
Many institutional insurance purchasers buy insurance through an insurance broker. While on the surface it appears the broker represents the buyer (not the insurance company), and typically counsels the buyer on appropriate coverage and policy limitations, in the vast majority of cases a broker's compensation comes in the form of a commission as a percentage of the insurance premium, creating a conflict of interest in that the broker's financial interest is tilted towards encouraging an insured to purchase more insurance than might be necessary at a higher price. A broker generally holds contracts with many insurers, thereby allowing the broker to "shop" the market for the best rates and coverage possible.
The main difference between collision and comprehensive coverage comes down to the question of what the driver controls. Collision insurance will cover events within a motorist's control or when another vehicle collides with your car. Comprehensive coverage generally falls under "acts of God or nature," or things that are typically out of your control when driving. These can include events such as a spooked deer, a heavy hailstorm, or a carjacking.