What is the difference among beta decay, beta plus decay (positron), and electron emission?

a beta particle is an electron
a positron is a positively charged electron

when beta decay occurs, the atomic number increases by 1 but the mass stays the same because because a neutron becomes a proton.
19/40K --> 20/40Ca + 0/-1e

in positron capture (electron capture), the atomic number decreases by 1 and the mass stays the same. a neutron becomes a proton.
20/40Ca + 0/+1e --> 19/40K

electron emission is beta decay

Beta decay is when an an electron antineutrino is emitted. Beta plus decay is also known as positron decay. In positron decay, an electron neutrino is emitted. Electron emission is the same thing as beta decay, but if your talking about field electron emission, it is when electrons are emitted because of an electromagnetic field.

Hope I helped :)