Loss Damage Waiver, Collision Damage Waiver, PDW and LLDW are all the same thing. They provide you with insurance cover in case you damage your hire car.
Liability Insurance Supplement or Supplementary Liability Insurance are both the same thing. It provides you with insurance cover in case you cause damage to other people or property as the result of an accident which is your fault. All car hire comes with the legal minimum of Liability insurance ($30,000) but this is not enough cover, so you need to supplement this with an additional policy. Most SLI policies provide cover up to $2million.
Personal Accident Insurance and Personal Effects Coverage refer to insurance cover for you personally and to your belongings you have on holiday. This would include any hospital treatment you required as a result of a crash (which was your fault) as well as theft or damage of your belongings while on holiday. Your holiday
travel insurance will probably provide sufficient coverage for both these aspects, so you would probably not need to buy the same insurance coverage through your car hire.
Although I think both Loss damage Waiver and Supplementary Liability Insurance to be essential, you are not obliged to buy them from the same company that provides your car hire. You might find that buying your car hire insurance from an idenpendent company works our cheaper for you. I usually get my car hire insurance as part of my travel insurance policy from American Express. Natwest also offer a car hire policy at a reasonable price (if you pay for the car hire with a Natwest credit card). Please ask about either of these if you want more info.
Regards
Rob