Combining two equations by addition or multiplication?

Hello all,

I have a seemingly simple question concerning the combination of two quadratic equations:

z(x) = x^2 + 2*x - 1

z(y) = 2*y^2 + 3*y + 1

What is the significance of combining these two equations by multiplying them together versus simply adding them together? I know if I take the product of the two equations, I will end up with a 2D surface described by equation z(x,y). But what is the difference between that and the equation obtained by adding them together, z(x,y)?

Any insight on this will be much appreciated.

Regards,

smpaladin