Yes, it is different. The Huckleberry Finn case alters the actual text. Were the reader none the wiser, he would think that the word "slave" was what the author originally wrote. The equivalent regarding "Money For Nothing" would be if all subsequent editions of the Dire Straits album had the word "******" replaced with something deemed less offensive. That isn't the case. The measures suggested concerning "Money For Nothing" are merely temporary and apply only in very particular circumstances (radio play). There is no permanent altering of the lyrics, simply a "bleep". Such "bleeping" has been customary for a long time, especially with hip-hop ("clean" versions).
Here's a blatant example that is especially relevant here. Anyone familiar with N.W.A. will know just how much editing was necessary to make this track "clean" without even listening to it. What's interesting is that, despite all of the "backwards" edits, the word "fag" remains intact: