If your wife hit the truck's drive shaft and ran over it in her vehicle then it normally would be considered by most car insurance companies to be a Collision claim rather than a Comprehensive claim. Comprehensive coverage does not tend to come with more benefits than your Collision coverage has.
In general, Collision coverage is intended to cover things that your vehicle strikes while Comprehensive coverage is intended to cover things that strike your vehicle. Basically Comprehensive is supposed to cover losses that are due to things other than collision or overturn.
Insurance companies' guidelines vary as do the terms of a car insurance policy but when you run over debris or a road hazard, like parts that have fallen off of a truck, it is typically considered to be a Collision claim, because your vehicle collided with the item.
If in your wife's situation the drive shaft fell off the truck and bounced up into her car's hood or windshield, it would most likely then be considered a Comprehensive claim. When debris strikes your vehicle or is acts as if a flying missile that hits your vehicle it normally fails under your Comprehensive coverages.
Your Collision and Comprehensive coverages may come with different deductibles if you set up your policy that way but the coverages themselves are very similar in that they both should pay for the damages to your vehicle or pay you actual cash value (ACV) for your car if it is declared a total loss. If one pays for towing charges then the other likely does as well or it may be that you have no towing coverage with your car insurance company unless you bought extra coverage called Towing and Labor.
Neither Collision nor Comprehensive usually comes with rental car reimbursement coverage. You need to purchase this extra coverage on your policy to be repaid (up to a certain stated amount per day) for renting a vehicle to drive while your car is being repaired or until a settlement offer is made for a totaled out vehicle.
Your agent or the insurance adjuster assigned to your claim should be able explain to you exactly why your auto insurance provider finds this to be a Collision claim and also if your car insurance policy coverages afford you the benefit of towing and a rental car.
If your agent is not able to explain to you what to do in this situation or fulfill your car insurance needs, contact a CarInsurance.com agent and they can explain not only insurance terms and explain claim procedures but also tell you how they can get you low cost car insurance.