Yes, it turns out the two things in the title of this post have comparable sizes. Who knew?
A neutron star is a very old star that has burned off most of its energy and then collapsed into itself. As a younger star (such as our sun) undergoes the nuclear fission reactions that make it glow, the energy released keeps all of that matter spread out to a very large distance. But if those reactions cease, the intense gravitational forces compress everything down to a shockingly small volume.
In the image above, that blue ball contains the equivalent of 500,000 Earths worth of matter, giving it an unimaginable density: a teaspoonful of the stuff would weigh a couple billion tons.
And yes, that shadow makes no sense whatsoever. But it looks good, and that’s what’s really important.