  The question whether the total gluon angular momentum in the nucleon can be
decomposed into its spin and orbital parts without conflict with the
gauge-invariance principle has been an object of long-lasting debate. Despite a
remarkable progress achieved through the recent intensive researches, the
following two issues still remains to be clarified more transparently. The
first issue is to resolve the apparent conflict between the proposed
gauge-invariant decomposition of the total gluon angular momentum and the
textbook statement that the total angular momentum of the photon cannot be
gauge-invariantly decomposed into its spin and orbital parts. We show that this
problem is also inseparably connected with the uniqueness or non-uniqueness
problem of the nucleon spin decomposition. The second practically more
important issue is that, among the two physically inequivalent decompositions
of the nucleon spin, i.e. the "canonical" type decomposition and the
"mechanical" type decomposition, which can we say is more physical or closer to
direct observation ? In the present paper, we try to answer both these
questions as clearly as possible.
