Yes, you're correct. They're different terms for the same thing. I've also seen (in old Thrifty literature) PDW, which is Physical Damage Waiver. They all waive the renter's responsibility for physical damage to the rental vehicle (most companies also waive associated fees, such as loss of use, administrative fees, diminution of value, etc.; most do not waive towing costs).

Technically, what AMEX and other credit card companies offer is not CDW. They can't "waive" damage charges any more than your insurance can waive damage charges, since they're not the ones charging you (the rental company is). AMEX and other card companies offer an insurance product that reimburses part or all (subject to limits and exclusions) of the damage charges charged by the rental agency.