In both, the fundamental definition seems to be "one who is collecting unemployment benefits."  That is, though, where the big difference lay, as German unemployment benefits (pre-Hartz IV, at any rate) are given without time constraint.  US unemployment benefits typically run out after 6 months.  Americans without jobs get categorized as "discouraged" after a certain amount of time and are statistically dropped from the labor force.  In Germany, they remain "unemployed."

Therefore, American unemployment percentages look nicer than German ones would for the same proportion of job-seekers.

I need to do a bit more research on it, but those are the basics.