The "Approach Climb" is essentially for the configuration that you would set the aircraft to if a missed approach was carried out during approach, i.e. Gear UP and the Flaps retracted to the "Go-Around" setting, typically a setting routinely used for Takeoff. With OEI, the minimum Gross Gradient is 2.1% (Note that PANS-OPS minimum obstacle-clear gradient is 2.5%, be careful!)
The "Landing Climb" is with ALL engines operating in the Landing Configuration, i.e. Gear DOWN" and Flaps left at the Landing Flap setting. Minimum required gradient is 3.2%.
In Short, Approach Climb is intended to cover you for a 1 Engine Inoperative Missed Approach, and Landing Climb for the All engines missed approach. (There's a bit more to it than that, but that's the basics).
Regards,
Old Smokey