Is there a difference between "regular" clinical depression and one that is the aftermath of a trauma, and/or Post Traumatic Stress Syndrome(PTSD) ?

Yes, there seem to be some differences when depression follows trauma, and this may eventually be designated a  subtype of depression. Recent discoveries suggest that trauma such as childhood sexual abuse, for example, may change the way that brain and body chemicals are produced for the rest of the survivor's life, unless effectively treated. There is an excessive secretion of "fight or flight" chemicals in reaction to the stresses of everyday life, which puts these survivors at much greater risk for developing "mental" illness, and takes a toll on health generally.

In a study of women who were put under mild stress by having to do arithmetic before witnesses, an overproduction of ACTH (a pituitary hormone that induces the adrenal gland to produce cortisol) was greatest in those with a history of childhood sexual abuse and depression - about 6 times the amount produced by women without depression and abuse.  Women with major depression, but without significant early trauma, had normal responses to stress.

Another difference that researchers have uncovered is that depression that accompanies a history of trauma tends to present as atypical depression with symptoms of oversleeping and overeating. There also seems to be a frequent link between childhood physical abuse and the development of mania. Also, some recent studies have compared patients with non-psychotic depression, and those with psychotic depression (that is, suffering strong delusions), finding that the latter were far more likely to have PTSD.

As we discover these differences, we are able to hone treatments, using the antidepressants we have with less trial-and-error, and to develop new ones to address the specific chemical processes that occur with different depression subtypes.