If you do quick exploration the retainer will bring bag random things (a lot of fish ^^) and it does NOT depend of the class.

For DoW/DoM, when i do 18h exploration with a WAR, I get some of the Mossy Stone item to craft i70 weapon, but he seems to bring only 5 out of 9 possible item. I got spear, axe, claws, invoker book and really rarely sword, he brang back nearly 5 or 6 of each (only 2 for sword) and never brang back the one for WHM, BLM, BRD, ERU.
So I think that the one I don't get may be gotten by other class of DoW/DoM.

(Botanist can bring the same as the WAR though)