Yeah - they are weird objects. A star has to be greater than about 8 solar masses to gravitationally collapse into a neutron star at the end of its life. Much more than ~30 solar masses and you get a black hole rather than a neutron star. Both these exotic objects are supernova remnants. When a large star runs out of fuel, it collapses bewilderingly quickly - a few seconds - producing a huge amount of exceptionally hot material (mainly as a result of mechanical bounce - first the core collapses, then the outer shells of the star go inwards at about a quarter the speed of light, hits the collapsed core, bounces, and comes out again very hot indeed).
Also, since a star spins (pretty slowly), as it collapses the spin speeds up, like a figure skater spinning on the ice can speed up, due to conservation of angular momentum. A neutron star can spin anywhere from once every few seconds up to about 1kHz, and emit a beam of radiation along its spin axis at the rotation speed. That was discovered in 1967 by a then research student called Jocelyn Bell in Cambridge UK using the radio telescope there. Initially tongue-in-cheek christened LGM for Little Green Men, she later figured out could be a spinning neutron star - now known as a pulsar. Her research supervisor Anthony Hewish won the Nobel prize for her work, and she got diddly squat.
The fate of our star is different - since it is below something called the Chandrasekhar limit for formation of a white dwarf (>~1.44 solar masses; he figured that out aged 19, back in 1930) it will progressively bloat and cool when it runs out of fuel, swallowing up all the planets to earth and beyond, and becomes a red giant. Lucky for us not for quite a while yet, even though our sun destroys 5 million tons of material every second in nuclear fusion. To put that into context, a 10MT thermonuclear bomb destroys 0.05kg.