We show that the Chen et al. approach, where physical and gauge degrees of freedom of the gauge potential are explicitly separated, allows one to define two types of gauge transformations. Measurable quantities can therefore be sorted into two sets, observables and quasi-observables, depending on how they behave under these two types of gauge transformations. Based on this classification, we discuss the observability of the different decompositions of the proton spin. In particular, we argue that many apparently contradictory claims spread in the literature can be reconciled, provided one specifies what type of gauge symmetry is considered.