Given the forum, I assume you're referring to the Flash Platform products.

To briefly summarize, the official Adobe Flash Platform product line consists of Tools, Frameworks, Runtimes, Services and Servers. Not all of them are particularly applicable to game development, and, of course, there are many third party libraries and tools available for working on the Flash Platform.

Starting with Tools, Adobe has three development environments, each targeted to a specific type part of the spectrum from coder to artist:

1. Adobe Flash Builder - (Previously called Flex Builder) An Eclipse based IDE, targeted primarily RIA coders using the Flex framework, but it also currently the most advanced ActionScript IDE, including a debugger and profiler.
2. Adobe Flash Catalyst - On the other end of the spectrum, this is pretty much just for designers wanting to create "interactive content", no coding required.
3. Adobe Flash Professional - The classic Flash IDE. This cuts right down the middle. It's part drawing and animation tool, part programmer's IDE. Far better at the former than the latter, none it has few equals as a rapid game development tools for those who master it and are willing to deal with its limitations.

The most popular alternative to these is FlashDevelop (http://flashdevelop.org). It is open source, and, though it's not as advanced in most ways as Flash Builder, FlashDevelop is quite usable. Its code completion and editing is at least as good as Flash Builder, but it lacks an integrated debugger or profiler. There is a debugger plugin, but it's not yet included with the official distribution.

Moving on to Frameworks, there's really only one official Adobe framework right now - Flex. It's actually a really sweet framework for application development, but not particularly useful for game development.

Looking next at Runtimes, there are two from Adobe:

1. Flash Player - The big one. This is one of the most widely distributed run time environments, second only to browser based JavaScript.
2. Adobe Air - Adobe's path to bring Flash based applications to the desktop. Currently there are some performance issues, but it's a viable way to package a Flash based game as a downloadable product, playable without an internet connection.

The Services and Servers provided by Adobe are unsuited to game development & hosting, and are more targeted to media streaming and database integration.

Obviously, Adobe also sells other tools that can be useful for game development, most notably their Photoshop line.