What are the differences amongst dates, prunes, and figs?

Dates are fruit from certain palm trees, prunes are the dried fruit of plum trees, and figs are fruit from the fig tree.

I beg to differ, there is an Italian prune tree growing in my back yard.

The fruit of certain plum trees is really only suitable for drying into prunes, just as you wouldn't produce raisins from your Bordeaux Grand Cru vinyard. The genus Prunus (in which are the plums) comes from the Latin for plum. The two words are sort of interchangeable - but the undried fruit is usually a plum, and the dried fruit a prune (and nasty in my opinion). Exception: the South African Prune, which is no relation to the Prunus trees anyway.