A black hole is more dense. In principle, the black hole exists all
at one point. So its volume is zero, and its density is infinite.
The mass remains the same, the star becomes more and more dense as the volume decreases
A black hole isn't a hole as such. It is an extremely dense dead star that attracts all matter into a tiny singularity that has a massive density.
It can either become a neutron star or a black hole. If the star is between 8 and 15 solar masses, it will become an incredibly dense neutron star. If it is more than 15 solar masses, it will collapse and become an even denser black hole.
A black hole originated as a star, that is, the star converted to a black hole.
When a star starts to run out of fuel, it will begin to cool, and as it cools, it begins to collapse. If a star is massive enough, there will come a point where the neutrons in the centre of the star can no longer withstand the force of gravity acting upon it. This then results in the star continuing to collapse further; it becomes more and more dense, and ultimately forms a black hole.
A "black hole" may be the most dense object. The problem with a black hole is that our mathematical understanding of physics breaks down at the event horizon of a black hole, and we don't know about anything inside.
A black hole in one sense can be considered the "inside out" end of a very massive star. When that star dies in a massive implosion of it's core, it becomes so dense that nothing - not even light - can escape it's gravitational pull (hence black holes cannot be seen, that's why they are called "Black Holes"). It started as a massive star, it ended as a black hole.
"Small but very dense" sounds like the description of a neutron star or "collapsed matter star". Theoretically, a black hole (the only thing more dense) has no physical size at all. So, "neutron star". If the neutron star is spinning rapidly, they are called "pulsars" for the radio-wave pulses that they generate.
A black hole does not create a star. A black hole is formed when a star dies.
A black hole has more mass than a neutron star, but if you are comparing volume it would depend on the mass of the black hole. A neutron star is estimated to be about 14 miles in diameter, which is larger than the event horizon of a black hole up to about 3.8 times the mass of the sun. A more massive black hole will be larger.
Black holes are created when a star runs out of fuel and collapses. That is a nova, A black hole is made when a neutron star goes SuperNova and the energy tears a hole in space, creating a strong gravitational singularity.
A neutron star or a pulsar, or a black hole.