I'm confused because gamma rays are classified as an electromagnetic wave. But why is neutron radiation not considered electromagnetic wave? I know Alpha and Beta, as well as positron and proton, is not considered electromagnetic wave because it can be deflected by magnetic or electric field (because they are + or -).
But a neutron is neutral, so why is it not electromagnetic wave? Can it be deflected too by electric and magnetic field? Is that why? Or is there another reason?
Electromagnetic radiation consists of electromagnetic waves (oscillations of the electric and magnetic field), whereas corpuscular radiation consists of actual particles. Certainly, wave–particle duality can make the distinction between waves and particles fuzzy. However, electromagnetic radiation (whether described as wave or as photons) is massless (its invariant mass is zero) and it travels at the speed of light. In contrast, the particles of corpuscular radiation have a non-zero mass and therefore a velocity below the speed of light. The particles of corpuscular radiation can be charged positively (e.g. α particles) or negatively (e.g. β− particles), or they can have no charge at all.
Neutron radiation is a corpuscular radiation because it consists of particles (i.e. neutrons). Neutrons are subatomic particles with no charge and a mass of $m=1.674\,927\,471(21) \times 10^{-27}\ \mathrm{kg}$ [source], which is slightly larger than the mass of a proton.
The kinetic energy of free neutrons can vary significantly. For example, the so-called fast neutrons, which are released during nuclear fission, have energies above $E_\text{kin} = 1\ \mathrm{MeV} \approx 1.6 \times 10^{-12}\ \mathrm{J}$. The thermal neutrons, which are used to initiate nuclear fission in moderated reactors, have energies below $E_\text{kin} = 0.1\ \mathrm{eV} \approx 1.6 \times 10^{-20}\ \mathrm{J}$.
Since, in classical mechanics, kinetic energy $E_\text{kin}$ is $$E_\text{kin} = \tfrac{1}{2}mv^2$$ where $m$ is mass and $v$ is velocity, the velocity of a neutron with a kinetic energy of $E_\text{kin} = 0.1\ \mathrm{eV} \approx 1.6 \times 10^{-20}\ \mathrm{J}$ may be estimated as $$\begin{align} v &= \sqrt {2\frac{E}{m}}\\[6pt] &= \sqrt {2\frac{1.6 \times 10^{-20}\ \mathrm{J}}{1.674\,927\,471 \times 10^{-27}\ \mathrm{kg}}}\\[6pt] &= 4.4\times 10^3\ \mathrm{m\ s^{-1}} \end{align}$$ which is clearly less than the speed of light.
Electromagnetic waves are oscillating electric and magnetic fields, oriented perpendicularly to each other and their direction of motion. According to quantum mechanics, the energy of an EM wave is quantized, and each quantum is called a photon (from which the idea of light as a particle is formed). If you look at an EMR spectrum, you will see all the different sort of EM waves categorized by their wavelengths—radio waves, microwaves, infrared, visible light, UV, x-rays, and gamma rays.
I assume you’re grouping gamma waves with alpha and beta particles because of nuclear decay, and thus assume that gamma waves are particles, just like alpha and beta particles are. But they aren’t exactly the same. Alpha and beta particles (and positrons and the like) are not EM waves not because they are charged and capable of being deflected by a magnetic field, but because they are simply particles with mass and volume—they are not pure energy as a photon is. That is what a gamma ray ‘particle’ is—a photon, or quantum of light energy. It is a particulate manifestation of an EM wave in the highest range of frequency, and is devoid of mass and volume.
That said, neutron radiation is not an EM wave because
It is a particle that has mass and volume, just like any macroscopic object you’re familiar with - I don't think a neutron is like any macroscopic object I am familiar with. Although it has a mass, and a volume (sort of) it doesn't behave like anything macroscopic.
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