The degree of B/B;{'} alternate cation order is known to heavily influence the magnetic properties of A_{2}BB;{'}O_{6} double perovskites although the nature of such disorder has never been critically studied. Our detailed x-ray absorption fine structure studies in conjunction with synchrotron radiation x-ray diffraction experiments on polycrystalline Sr_{2}FeMoO_{6} samples with various degrees of disorder reveal that a very high degree of short range order is preserved even in samples with highly reduced long range chemical order. Based on these experimental results and with the help of detailed structural simulations, we are able to model the nature of the disorder in this important class of materials and discuss the consequent implications on its physical properties.