Seems one may have been reliant on the other.

depend
early 15c., "to be attached to as a condition or cause," a figurative use, from M.Fr. dependre , lit. "to hang from, hang down," from L. dependere , from de- "from, down" + pendere "to hang, be suspended" (see pendant).

rely
early 14c., "to gather, assemble," from O.Fr. relier "fasten, attach, rally, oblige," from L. religare "fasten, bind fast," from re- , intensive prefix, + ligare "to bind" (see ligament). Sense of "depend, trust" is from 1570s, perhaps via notion of "rally to, fall back on."