Pulsars form a specific class of neutron stars that emit radio waves, gamma rays and x-rays periodically.
Stars that have a mass of 1.4-9 times the mass of the sun undergo supernova explosions that cause the outer core to be detached and blasted into space, while the inner core collapses under strong gravitational force. In fact the gravity is so strong that protons and electrons fuse together and the left-over star is left with nothing but neutrons and hence the name neutron star. These stars are extremely small in size, very-very dense and spin at high rates (from 1 revolution in 4.3 second to 11,000 revolutions per second). During the rotation, the magnetic poles of some of the neutron stars emit high-energy beams, composed of material from companion stars. These emitters seems to pulse when observed from Earth and hence are called pulsars.
So all pulsars are neutron stars, but not all neutron stars are pulsars.