Variance and 2 point function in perturbation theory

When we try to find the statistical correlation of some perturbation between two positions, we always calculate the quantum 2-point function. Are these two concepts really the same?
Also, people say vaccum fluctuation is gaussian. For normalized fields, we always use Bunch-Davies initial condition ##\frac{1}{\sqrt{2k}}e^{-i k \tau}##. So in which sense do we say it is gaussian?
Thanks! Any reference would be appreciated!