Yes, it's rather funny, really, that next to no one realized the snake that Harry set free in Philosopher's Stone turned out to be Voldemort's finnal horcrux, Nagini -- J.K. Rowling
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This is actually not true. It's just a rumor that started on Tumblr. The snake Harry rescued from the zoo was a constructor boa and it specifically said so and also, he was Brazilian, but was bred in captivity, which means he never left the zoo before Harry saved her. Nagini was a viper, a completely different snake.
Voldemort met Nagini during his exile in Albania. Like you already know, on the night he went to Gordic's Hollow to kill Harry and Lily sacrificed herself for him, the curse rebounded, leaving Voldemort as nothing more than a bodyless phantom. He then went to Albania where he possesed snakes and inhibited their bodies. Nagini was the last Horcrux Voldemort made and he made her in 1994 by killing Frank Bryce (beginning of Goblet of Fire) with the Killing Curse.
As far as the movies go, there were no actual snakes to begin with. Both the snake from the 1st movie and Nagini were CGI animation. The snake from the 1st movie was a Dumeril's Ground Boa and Nagini was a Reticulated Python, although her appearance changed after the 5th movie where she strongly resembled a Burmese Python.
So in fact. they are 2 completely different snakes.

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Facts about Harry Potter that you didn't know
RandomIn this book you'll finds some facts about Harry Potter characters that you probably didn't know. Enjoy! Disclaimer: I own nothing