Can anyone explain clearly 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.