What is the difference between a photon and a neutrino? Why are they not considered photons?

Photons are gauge bosons of the electromagnetic interaction, Since this is an infinite range interaction, their mass is required to be zero. Neutrinos are matter particles, like electrons. The photon is more like a W, since both are bosons

A photon is a boson which means that it obeys the Bose-Einstein statistics. It has zero charge and a spin of 1. It is the quanta of the electromagnetic field. It also has zero mass which means that it must travel at the speed of light. It is also its own anti-particle.

A neutrino is a fermion which means that it obeys the Fermi-Dirac statistics. It is also a lepton which means that it doesn't interact via the strong force.

The electron is also a fermion, along with its heavier generation particles the muon and the tauon. There are three generations of neutrino, the electron neutrino, the muon neutrino and the tauon neutrino. They have no charge and a spin of 1/2. Each neutrino has an anti-neutrino antiparticle.

Electron neutrinos are emitted in radioactive beta decay and carry away some of the energy released. In beta decay a neutron decays into a proton, an electron and an electron antineutrino.
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Neutrinos are thought to have zero mass and travel at the speed of light. They rarely interact with other particles of matter. This is still open to debate. It is also thought that neutrinos oscillate between the electron, muon and tauon particles.