Here are a few details:
HRC7013: 13hp, 36" or 48" deck. Twin hydrostatic drive motors. Based on Bunton frame/deck and final assembly done at Bunton Co. in Louisville, KY.
HRC7018 / HRC7020: 18/20hp with 52" or 60" decks. Twin hydrostatic drive motors.
HRC7113: Gear-drive version (lower cost). Slightly different controls.
The HRC7013 (first built in 1993) is the oldest, and generally speaking, the older the unit, the more likely parts will be discontinued or No Longer Available. For example, the carburetor for the original HRC7013 is discontinued.
Caveat: I work for Honda, but the preceding was my opinion alone.