Photons are something of a special case because they are massless. Gravitons, too. As bosons, their interactions are not limited by the Pauli exclusion principle, so they can not annihilate each other. They interact through different means (electromagnetic). They're both because they only have the common properties of particles and their antiparticles.
It's basically like saying "the number 0 is its own negative number". It's correct according to some definitions, but not useful.
Physicist here. You are confusing things. Having rest mass or Pauli-exclusion principle has nothing to do with qualification of being an anti-particle.
Z boson, for instance, does have mass and is its own anti-particle.
> It's basically like saying "the number 0 is its own negative number". It's correct according to some definitions, but not useful.
Photons have zero charge; an anti-particle has negative of the particle's charge (and at the same time, same rest mass and spin).
It's basically like saying "the number 0 is its own negative number". It's correct according to some definitions, but not useful.