The antiparticle of a neutron is called an antineutron, while the antiparticle of an electron is a positron. It's clarified that the antiparticle of a proton is an antiproton, not a positron. Most particles have their antimatter counterparts prefixed with "anti," such as antineutron for neutron. The discussion suggests using online resources like Google or Wikipedia for further information. Understanding these relationships is crucial in particle physics.