What are the differences between AdaDelta and RMS prop in Keras (if any)?

Question

I have read many references which suggest that RMSprop and Adadelta are basically same, just developed independently. However, Keras has two different classes for it. Also, it allows RMS prop to have momentum but not AdaDelta. In this link as well, RMSprop and AdaDelta have different trajectories.

I want to understand the mathematical difference between RMSprop and AdaDelta in context of Keras.