CDW and LDW are usually two different things, but often come together. I'm not an expert, because with US credit cards and personal insurance in the US I don't have to be (I get sufficient cover from either alone that I can/should decline CDW/LDW). But I'll do my best. Usually there is a deductible (excess) on either - which is one of the reasons I always decline, as most decent US credit cards provide no-excess coverage on all but especially premium vehicles. In the case of these cards, it's important to note that their coverage is invalidated if you accept CDW/LDW from the renting agency... so at least in my situation I'd almost always end up paying more to receive less complete cover.

Have you tried ringing up Avis (using their US number since they'll be most familiar with US cover) and asking them? I see you called the airport location, and they couldn't answer you (which surprises me, but maybe they don't have access to your reservation until the day you pick up the car). I should hope calling Avis reservations in the USA and asking the relevant questions for cover pertinent to your booking should sort it out... If they say you can only be informed (or choose additional cover) upon rental pick-up, I'd be inclined to ask for someone who can make it more clear the terms of what you already have reserved, as you need to know that before you can find out whether your own travel cover, personal cover, etc. applies.