Understanding brain function, constructing computational models and engineering neural prosthetics require assessing two problems, namely encoding and decoding, but their relation remains controversial. For decades, the encoding problem has been shown to provide insight into the decoding problem, for example, by upper bounding the decoded information. However, here we show that this need not be the case when studying response aspects beyond noise correlations, and trace back the actual causes of this major departure from traditional views. To that end, we reformulate the encoding and decoding problems from the observer or organism perspective. In addition, we study the role of spike-time precision and response discrimination, among other response aspects, using stochastic transformations of the neural responses, here called stochastic codes. Our results show that stochastic codes may cause different information losses when used to describe neural responses and when employed to train optimal decoders. Therefore, we conclude that response aspects beyond noise correlations may play different roles in encoding and decoding. In practice, our results show for the first time that decoders constructed low-quality descriptions of response aspects may operate optimally on high-quality descriptions and vice versa, thereby potentially yielding experimental and computational savings, as well as new opportunities for simplifying the design of computational brain models and neural prosthetics.