algebra precalculus - Why is the graph of $x=y^2$ and $y=sqrt{x}$ not the same?

So if you take $x=y^2$ and get the sqrt of both sides you get $y=\sqrt{x}$ so they are the same right? But when you graph them, $y=\sqrt{x}$ only shows the positive $y$ values because you can't sqrt a negative number because no 2 same numbers multiplied together are negative and what not. And of course $x=y^2$ shows both positive and negative $y$ values. So why does this happen with this?

EDIT: My girlfriend pointed out that in $x=y^2$ the $x$ technically cannot be negative cuz if the $y^2$ will never be negative. But why do graphs show the negatives? And I forgot to show you the site where it graphs the negatives: http://www.coolmath.com/precalculus-review-calculus-intro/precalculus-algebra/09-sideways-parabolas-01

Answer

Simply because $x=y^2$ doesn't imply that $y=\sqrt x$.