Yes Jeff, that is the flashplayer for Internet Explorer. As stated already, Youtube and many other sites are now using the HTML5 player and most modern and up to date browsers work with it.

As an aside, Adobe are doing a lot of work to try to fully secure flash player and updates to more secure versions are available, just check on the Adobe flashplayer site.

Shockwave flash player was the older name, Adobe just shortened it by removing the shockwave bit.