The IK Blend T and IK Blend R (previously called Reach) sliders in the HumanIK Controls let you decide which solution (IK or FK) your skeleton follows.
When you set keyframes on a Control rig, both the IK and FK solutions are keyed. By default, the Align/Synchronize Control Rig feature synchronizes the Control rig, causing the IK and FK solutions to appear on top of each other in the scene.
The interpolation of the IK and FK solutions do not match because IK effectors are global and FK effectors are local to the hierarchy. You can visualize this by turning the Align Control Rig option off ( > Edit Control Rig > Align/Synchronize Control Rig).