What is the difference between distributed representations and factors of variation in deep learning
Usually, factors of variation are independent from each other. However, sometimes in feature extraction, some combination of these factors can be helpful to detect better and accurate features to explain the behavior of the observation.

Therefore, factors of variation are used to explain distributed features, and their relation likes the relation between basis of a space and a vector which is defined in the space using these basis or prime factors.

Although, observations change base on the factors of variation and distributed features, distributed features change base on the factors of variation. 
In the other words, features of variation are prime factors, and distributed features are defined base on the prime factors.