A neutron star is the "end of the line" for a giant star that exploded as a supernova. The material in a neutron star is packed so densely that a chunk of it the size of a cigarette package would weigh thousands of tons. It spins rapidly, at a steady rate (they are sometimes called "radio beacon stars").
I suggest you do some reading on both, to get an idea what a neutron star really is, and what a supergiant is. For a start, some differences are: their diameter; their density; the fact that a neutron star no longer produces any energy.
Neutron (smallest) Dwarf Medium Giant Super Giant (largest)
Stars may collapse to such a degree, perhaps after a supernova, that, in the core, electrons are squashed into the nucleus, reacting with protons to form neutrons. A star of this collapsed state is called neutron stars.
When compared to the other stars, the Red Giant Star are very minute. There are other stars that are very large by far as compared to the Red giant stars.
I suggest you do some reading on both, to get an idea what a neutron star really is, and what a supergiant is. For a start, some differences are: their diameter; their density; the fact that a neutron star no longer produces any energy.
Smaller stars like our own expand into a red giant and then eventually collapse into a white dwarf, the more larger stars like a bright giant star expand into a hyper giant or a super giant. Super giant stars can go supernova and collapse into a neutron star, a white dwarf, or a black hole. The hyper giant stars go hypernova and make a gamma ray that eventually ends into a black hole.
The oldest stars are now mostly either white dwarfs or neutron stars. A few of the largest may be black holes.
It depends on its size. Smaller stars- main-sequence, red giant, planetary nebula, white dwarf, black dwarf Bigger stars- main-squence, red giant, supernova, neutron star.
Actually if a star is medium or low mass is will run out of fuel and turn into a red giant, once the stars atmosphere slowly drifts away and the core is remaining it will eventually become a white dwarf For more massive stars it will turn in to a super giant the will cause a supernova, after the supernova the star can either a black hole or a neutron star
Some massive stars will become neutron stars. When massive stars die they will either become neutron stars or black holes depending on how much mass is left behind.
All "pulsars" are neutron stars - it's just "we" term pulsars as neutron stars who's orientation towards us shows the beam of electromagnetic radiation. Other neutron stars who's orientation, do not point towards us are not called pulsars, although they exhibit the same characteristics.
Any two types of star can be gravitationally bound with another for instance you can get neutron-neutron pairs you can get two yellow stars or you can get a red super giant with a normal star so long as they are in gravitational equilibrium any two can be a paired star