What is the difference between differentially expressed genes and deregulated genes?
Any gene whose gene expression differs significantly from some reference is considered to be differentially expressed. I think the most common representation of differential expression is the volcano plot, where you're plotting the fold change or log2 fold change against the -log10 p value assigned that gene. 

This means a couple of things: One, you need a sufficently large sample size that you can actually get statistics, and two, you need a sufficient reference sample which will act as your baseline. 

If a gene is degregulated, however, the expression is aberrant. In order to characterize aberrant expression you need a normal sample or accepted reference sample, and the sample of interest. This might be as simple as tumor vs normal tissue from the same patient.