Generally, in my experience, the same people recite kaddish d'rabbanan and kaddish yatom in davening. [Kaddish yatom is said after reciting psukim, such as a perek of Tehillim, while kaddish d'rabbanan is said after reading Mishnaic/Talmudic statements.] However, in the morning [teen] minyan i've been going to recently, i've noticed that often the gabbai will ask one of the other adults to say kaddish d'rabbanan but not kaddish yatom. Noone else says either kaddish.
(This is nusach Sefard, so the order at the end of davening (after kaddish shalem) goes shir shel yom, kaddish yatom, ein kelokeinu etc, kaddish d'rabbanan, barchu, aleinu, kaddish yatom.)
What's the difference between the two kaddishes, and why would someone say one but not the other?