I believe you will find they are different players - I have both installed on my pc's. Flash Player latest version is 9.0.28 - Shockwave Player latest version is 10.1.4.020. Not sure what each does, but believe you might consider keeping both.
The difference is (per Adobe site): "The difference between the Macromedia Flash and Shockwave Players
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 multi-user games. Through Xtras, Shockwave Player is also extendable to playback custom-built applications."
I was having problems with Flash Player playing videos at some sites and blamed Adobe Flash Player, IE7 and/or the sites. Turns out it was none of them causing my problem. Rather, it was a program I had installed (Comodo Verification Engine) which was running and not compatible with Flash Player. I unistalled VEngine and all is well again with Flash Player sites and videos. You might check your installed programs to see if you also have some conflicting programs which will not let Flash Player run properly at all sites. Just a suggestion, but one which worked for me and I had previously tried everything to solve this problem.