The way Chad explained it, a positron is kind of like a subtype of a beta (B).
Beta (B) particle is an electron with a mass # of 0 and an atomic # of -1.
In beta decay/emission, a beta particle aka electron is emitted from the nucleus and it turns a neutron into a proton.
A positron is a positively charged electron, so it has the same mass # as an electron (aka beta), but with a positive charge. So the mass # is 0, but the atomic # is +1.
In postron emission, a positron is emitted from the nucleus and it turns a proton into a neutron.
Hope this helps 🙂.