In my mind, you get a quote for a specific service. I'd want a quote for work done on my car. I don't really care to know HOW they do the work, or the thought process behind it. I just want the price and what they're doing. Most quotes are small (1-2 pages) and just list the price and what is included.
On the other hand, a proposal seems to me to be a much more detailed document. Personally, my proposals are sometimes 20 pages and I go into the company background, problems they face, how we can help them solve them, our solution, price, references, and even descriptions of the process itself so they know what to expect.
I get people that actually just ask for a quote - they tell me they just want a price. I tell them to go somewhere else... because of the amount of time involved in really understanding someone's situation and developing a solution to their problems. I'm not going to spend that much time just to end up competing on price.