What’s the same and what’s different about the following pairs of equations?

\(y=x^2-4\) and \(y+x^2-4=0\)

\(y=4-9x^2\) and \(y+4=9x^2\)

\(2y=4x^2-6\) and \(-(y-3)=2x^2\)

If you were given the following picture, could you suggest the equation of its pair?

How about if you were given this picture instead? Could you give the equation of its pair?