Answer: Because they rotate really fast.
First, it is necessary to clarify what is a pulsar (pulsating star) and what is a neutron star:
A pulsar is a neutron star that emits very intense electromagnetic radiation at short and periodic intervals due to its intense magnetic field that induces this emission.
A neutron star, is the name given to the remains of a supernova. In itself it is the result of the gravitational collapse of a massive supergiant star after exhausting the fuel in its core.
Neutron stars have a small size for their very high density and they rotate at a huge speed.
So, the way to know that a pulsar is a neutron star is because of its high rotating speed.
Nevertheless, it is important to note that all pulsars are neutron stars, but not all neutron stars are pulsars.
