Below are some hastily sketched thoughts, by no means complete, on the distinction between computational neuroscience and neuroinformatics.
Computational Neuroscience: The field posits computational candidates for mechanisms by which the brain carries out a certain function. When we say computational candidates, we loosely talk about algorithms. I think algorithms have two or more theoretical aspects. I'll try to articulate those below.
First, the goal of the function performed by the brain must be articulated by a cost function. For example, if the goal is reaching out for an object and grasping it, then the cost function could minimize muscular effort, minimize the #neurons needed to encode the task, or minimize the error rate of the task assuming that it is performed several times. Sometimes, the cost function need not describe a very specific task such as grasping, but could describe a general organizing principle of the brain - such as minimize energy consumption, minimize the use of connective tissue, etc.
Second, the process by which the cost function is optimized must be articulated, keeping in mind that such a process must be feasible in the wet brain. The wet brain provides structural and functional bounds on what a candidate algorithm can and cannot do.
With these basic ingredients, the flavours then vary because the choice of level of description can be vastly different. Someone can talk about how ion channel ratios on the cell membrane are optimal for grasping, whereas someone else can talk about why the number of cortical areas devoted to grasping the brain is optimal. Both these optimalities could be treated computationally by using selective pressures during evolution, or selective pressures during brain
development as explanatory variables. To complicate matters further, optimality in the brain can be posited at the level of evolution, brain development, learning (plasticity), and adaptation.
Neuroinformatics: The field is concerned with issues of data analysis and visualization of neuroimaging data for human interpretation purposes. The algorithms applied here (such as ICA/CCA/ridge regression etc.) need not conform to any constraints posited by the wet brain. The field does not aspire to explain how the brain performs a certain function - it just aids the process of evidence accumulation, which is of course important for theoretical and CNS because otherwise we wouldn't have phenomena to explain and our theories cannot be validated. In this sense neuroinformatics is a tool for experimental neuroscience.
9 months ago