Fireworks is more a collection of stock graphics and widgets geared towards people who want to make quick mockups and such. As a design tool it doesn't even come close to Flash.
No. Fireworks was a hybrid vector/bitmap editor specifically designed for web design. Flash is a vector based animation suite that originally included a javascript-based scripting language call actionscript.
You're right about Fireworks. Some people do like to use the Flash authoring environment for general web graphic work, even though that's not its primary intent. A friend of mine still uses it for all of his web tutorials and book diagrams. (Flash has tools for exporting single frames in a variety of image/vector formats.)
That's where Fireworks ended up. But it started off as a graphics editor for Flash.