Alpha particles: matter particles made up of clusters of 2 neutrons and 2 protons - basically they are heium nuclei - it is believed that protons and neutrons within the nucleus are arranged in clusters like this as they are so stable.

Beta Particles: matter particles that are identical to the electrons that are found orbiting the nucleus.. Yet they emanate from the nucleus (which doesn't contain electrons!). All experiments with beta particles show them to be identical to orbital electrons - mass and charge are identical. They are produced when a neutron breaks down and becomes a proton.

Gamma Photons: packets of high energy electromagnetic radiation... pure energy, no matter! High frequency and high energy. The only sort of electromagnetic radiation that comes from the nucleus is the gamma ray.

Antimatter Beta Particles (Positrons): yet they emanate from the matter in the nucleus! These are only given out by the nuclei of nuclides that have too many protons to be stable. These have only been discovered since we have been able to artificially 'make' isotopes that did not occur naturally on Earth during the last century. Some of these decayed to produce these antimatter particles. If a positron meets up with an electron they annihilate each other. and gamma rays are produced (but that is only tackled at Advanced level!).