I suspect the phrase is a cliche often used to sound scientific and sometimes by folks unaware, like how description of growth as “exponential” is a cliche used by non-mathematical discussion.
I agree with this. As a layman, I've always understood "orders of magnitude larger" to just mean "way too big" and "exponential" growth to imply "out of control".
x^2 and 2^x manifestly both involve exponents, so I think it's valid - outside math class - to call anything involving accelerating growth "exponential".