Both amazing space objects as we know are formed by collapse of a massive star under it’s own gravitational forces the only major difference is that a neutron star is formed when a star collapses 14 to 25 times of mass of our sun while a blackhole is formed when a star more than 25 times of mass of our sun collapses under it’s own gravity after it goes supernova. Another logical observable difference between them is their ability to let escape the light. While both objects are few of the dense objects present around in space obviously with strong gravitational fields, Neutron stars unlike Blackholes do not have strong enough gravitational pull resulting in, escape of light. This is due to the mass concentrated at their cores in case of Blackholes it’s called “singularity”. Current theories state a singularity has infinite mass while a neutron star finite mass compacted in very less volume making it dense. As we know the relation between density, mass and volume. More the density more the mass, but less the volume or more mass in less volume results in higher density and here as a neutron star holds lot of mass compressed in very tiny volume making it super dense and on other hand Blackhole having theoretically infinite mass in a very less volume, it is super duper dense.

As for how astronomers identify them , there are plenty of methods for that purposes but easily said Neutron stars are pulsing stars and are pretty bright so they are pretty observable as other stars. As for Blackhole they are hard to detect like finding any other object in space. But they can be found by observing their effect on surrounding matter in space most notably their effect on light as their strong gravity can bend light and their accretion disk.