George didn't write the Game Of Thrones TV show, it was written by David Benoiff and D.B. Weiss. RR Martin wrote 1 episode in each of the first 4 seasons, but then he completely stopped to focus more on writing the books.
He did produce it, which means he had some creative authority to approve or disapprove ideas. As I understand it, the show tries to stay true to the books in most cases but some things are changed, either because it's better for TV or just because the writers had a different idea. Also, the last couple seasons passed Martin so while I'm sure he gave them a direction, they're the ones who decided what to do. Might be why the final season feels so drastically different than the rest.
Anyway, books are 99.99% of the time gonna be better than the show or the movie. I like books being translated into tv series better, as you get a lot more screen time to fill it out. A movie, you get 2.5 hours tops usually. A TV show, even just a simple 10 episode one like Game Of Thrones is, you get about 10 hours to work with and you can fit so much more in. But even still, not everything makes it.
Also, don't read them out of order. It's so easy to get them in order, don't mess up your story experience by jumping around randomly.