Positron emission = emission of a positron and a neutrino when a proton is convert into a neutron. The total number of particles in the nucleus doesn't change, -1 proton +1 neutron
It's a spontaneous reaction for some nucleus.
Positron = e+
O-15 --> N-15 + e+ +ve
Electron capture= A nucleus absorb an electron while a proton is convert in a neutron and emit a neutrino. The total number of particles in the nucleus doesn't change, -1 proton +1 neutron
Al-26 +e- --> Mg-26 + ve
Electron capture and positron emission are two mechanisms to explain the decay of some unstable isotopes. Electron capture is usually observed when the energy difference between the initial and final state is low. Mainly because of the larger amount of kinetic energy need for the expulsion two particles with the positron emission mechanism.