You're correct n^2 is polynomial, not exponential. It was just an exaggerated figure of speech. BTW, O(n) and O(n log n) are also polynomial; it just doesn't have the punch to it.
"Exponential" is indeed misused.
Half the time I hear it, it is lower, like quadratic or cubic. The other half the time is higher, like combinatorial.
But even without any scaling factors, don't underestimate the size of the numbers involved. If you had two threads, one simply counting up to some n! upper bound, and the other up to 10^n - how long do you think the minimum problem size would take for the "slow" combinatorial to actually be slower than the exponentiation? Hint: at 4GHz and 1 op/cycle... Let's just say I'm not holding my breath that our species will still be around then. And even a tiny scaling factor to the mix...
I mean, if you're trying to estimate computational complexity at least, this nuance seems pointless.
But quadratic vs. exponential really matters, with plausible parameters.
I'm curious if the rise of quantum computers will make the differences between exponential and combinatorial meaningful in a practical sense.