The two numbers that describe a nucleus are its atomic (proton) number and its mass (nucleon) number. Each type of radioactive decay changes them in a different, predictable way.
An alpha particle is made of two protons and two neutrons. When a nucleus emits one, its mass number goes down by 4 and its atomic number goes down by 2. In β- decay, a neutron becomes a proton and an electron, so the atomic number goes up by 1 and the mass number stays the same. In β+ decay, a proton becomes a neutron and a positron, so the atomic number goes down by 1 and the mass number stays the same.
Gamma radiation carries away energy only, so neither number changes. If a nucleus emits a neutron, it has lost one nucleon that is not a proton: the mass number goes down by 1 and the atomic number stays the same, a change of zero. A change in atomic number means a different element is formed.