You are mixing up different concepts. A RNN is not the same as a R-CNN.
A RNN is a Recurrent Neural Network, which is a class of artificial neural network where connections between units form a directed cycle. This allows it to exhibit dynamic temporal behavior. The following image shows a simple representation of a RNN Cell.

A R-CNN is a Region-based Convolutional Neural Network. It is a visual object detection system that combines bottom-up region proposals with rich features computed by a convolutional neural network. Casually said the R-CNN proposes a bunch of boxes in the image and see if any of them actually correspond to an object. It computes these proposal regions with a selective search algorithm. The following image shows the architecture of a R-CNN:

So, to answer your question: A R-CNN is simply an extension of a CNN with a focus on object detection, while "normal" CNNs are usually used for image classification.