SQL is a language that is not particularly well defined, nor essential to solving problems. What you're referring to as a "well defined way of thinking" is the relational model. There have been relational databases that did not use SQL as their query language, and although they're not widespread, the same points the NoSQL community makes against e.g. Postgres could be made against them.
Like most buzz words, its popularity has overshadowed it's usefulness. I agree that a word to categorize these recently popular non-relational databases would be handy. But nosql is really not accurate. Unless you abandon all attempts to interpret it literally. When I see "nosql" that now tranlates into "that group of recent and fashionable databases which are primarily key/value stores with some traditional database features added in to varying degrees". So at least it means something (to me anyway), and it's abstracting quite a mouth full. Much better than "Web2.0" was. That always just translated simply to "ajax with nice UI" for me, but I saw the term used in so many ways that didn't fit that definition.
"that group of recent and fashionable databases which are primarily key/value stores with some traditional database features added in to varying degrees" is exactly what the term means.
Yeah, I think that's good. It's kind of like the term "Modernism," which makes no inherent sense but made sense when it was coined as a response to particular styles that came before it and were seen as, well, not modern enough. (Art people will tell me I'm wrong, but close enough.)
NoSQL refers to the databases that are proposed as alternatives in areas where programming culture had gotten used to thinking that the only solution was an ACID-compliant relational database. It means, "hey, this isn't the model you're used to, but give it a try anyway." You can't figure out the word without knowing the culture it emerged from.
