The remake of The Clash of the Titans is radically different from the original, but does keep a couple of elements the same. Why did Louis Leterrier decide to have the remake be so radically different and introduce other elements into the movie?
Louis Leterrier was a huge fan of the original film, but, as he put it:
I watched the original again. I went to a shop and bought the DVD and the stuff I love was still there. But it’s funny: memory is the best editor. So it was like, Oh, really? This was in it? It’s that simple? He goes on a journey because he fell in love with her? Really? I felt like what needed the most work was not the creatures, because they were fantastic (and, yes, we use different technology to bring them to life). It was really the story and the motivation. Why would this guy go on this suicide mission, this impossible mission, for the love of a princess? That was not working for me.
Therefore he kept some of the principal characters and monsters, but created a new version of the story. Incidentally, it should be noted that his film was effectively butchered in editing by the 'suits' - and Io's arc was drastically altered to make her Perseus' lover, not his sister as originally filmed. You can read more insights here: Vanity Fair Article on the Clash of the Titans Remake