No.......not the same.
Media edition is rather pricey. It's Microsoft's attempt to get into the TiVo side of things. I imagine that eventually they'll put up a hard fight, but I don't think that this current version threatens TiVo/DVR in any way just yet.
XP corporate edition is simply a version that doesn't require activation via Microsoft & is usually paid for up front by larger corporations whose IT dept simply needs 1 copy that they can put on hundreds of computers & don't need to be calling MS every time they fire up a new system.
I have every edition of XP except the media edition.........(maybe I need to add that to my collection??) Funny enough, however, I still have XP-home on my 2 Dells only 'cuz I'm lazy. XP's a good o/s any way you slice it. If you want Media edition, just be prepared to pay heavily for it.
Bill Gates wants *your* money................