Can anybody tell the difference?
Seems Adobe has many Web Players.
Why they wants to confuse their users when they could have various types (plug-in, standalone, debug) of single player which has it all.
Shockwave Player: see http://www.adobe.com/products/shockwaveplayer/
Flash Player: see http://www.adobe.com/products/flashplayer/
The standard installation for most users is the browser add-on to view web content.
To view local content you will need the standalone player.
Developers will need the debug player to debug their content.
Not that it totally clarifies the case, but here's what the resource over here tells:
Flash and Shockwave Players are both free Web Players from Adobe. Together, they bring you the best rich media content on the Internet. Each has a distinct purpose. Flash Player delivers fast loading front-end Web applications, high-impact Web site user interaction, interactive online advertising, and short to medium form animation. Shockwave Player displays destination Web content such as interactive multimedia product demos and training, e-merchandising applications, and rich-media multiuser games. When you download Shockwave Player, it automatically includes Adobe Flash Player.