The use of blade individual pitch control (IPC) offers a means of reducing the harmful turbine structural loads that arise from the uneven and unsteady forcing from the oncoming wind. In recent years, two different and competing IPC techniques have emerged that are characterised by the specific loads that they are primarily designed to attenuate. In the first instance, methodologies, such as single-blade control and Clarke transform-based control, have been developed to reduce the unsteady loads on the rotating blades, whilst tilt-yaw control and its many variants instead target load reductions in the non-rotating turbine structures, such as the tower and main bearing. Given the seeming disparities between these controllers, the aim of this paper is to show the fundamental performance similarities that exist between them and hence unify research in this area. Specifically, we show that single-blade controllers are equivalent to a particular class of tilt-yaw controller, which itself is equivalent to Clarke transform-based control. This means that three architecturally dissimilar IPC controllers exist that yield exactly the same performance in terms of load reductions on fixed and rotating turbine structures. We further demonstrate this outcome by presenting results obtained from high-fidelity closed-loop turbine simulations.