Your standard black hole is indeed the remnants of an extremely large, collapsed star, with the remnant sitting somewhere between 5-20 times more massive than our own sun. However, if we let nature produce a black hole, the black hole that is produced at the end of a supernova explosion is actually significantly less massive than the star that it once was.
Part of the drop in mass between star and black hole comes in the years before the supernova, when the star typically sheds a sizable fraction of its mass. Since the star has expanded so much as part of the red giant phase, it only has a loose gravitational grasp on the outer layers of its atmosphere, and they are easily pushed away from the star by the star’s stellar wind. Our sun has a stellar wind as well, and it’s one of the reasons Mars is still losing its atmosphere to space - it’s also the reason Earth’s magnetosphere is such a nice feature of our planet; we’re protected from this kind of atmospheric blasting by the sun. However, the Sun’s stellar wind is dragging many fewer particles along with it, compared to a red giant star, so the sun’s mass loss is much less than it would be if it were a red giant.
The star has pre-emptively lost some of the mass it contained before it became a red giant, but there’s also the supernova explosion itself to consider. A good chunk of the material that was left within the star goes blasting outward, fast and hot enough to barrel into any gas and dust nearby and produce X-rays. It’s really only the very core of the star that stays put, and can be compressed into the black hole.
If the mass of the star is actually only partially transformed into a black hole, then I’ve actually made the paradox in your question worse. How is the gravitational pull of a much bigger star (which light can escape from) so much weaker than a black hole made of only a fraction of the star (which light can’t escape from)?
The gravitational pull from a large object on a small one, at any point in space, is only determined by the mass of the heavy object, the mass of the smaller object, and the distance between the centers of the two objects. So, by this logic, if you were a cosmic wizard and replaced the sun with a black hole of equal mass, none of these parameters have changed for the planets. The planets haven’t changed their mass, or their distance from the center of the solar system where the sun used to be, and if the sun and the black hole are the same mass, then the whole system is gravitationally identical.
Obviously, there are some cosmetic differences between the black hole and the star in this scenario, but gravitationally speaking, differences only arise when you start to get very close to the objects. At the surface of our sun, which is where light escapes from the star and streams out towards the rest of the Universe, we are still 432,700 miles (696,000 kilometres) away from the center of the sun. A black hole, on the other hand, is a much denser object, so you can get far closer to its center while still having the entire mass of the black hole to contend with. It’s this density that makes the difference between light being able to escape or not.
For our magical swap scenario, you would have to get within 1.83 miles (2.95 kilometers) of the coordinates marking the very center of the Sun (or where it used to be) before you would cross the event horizon, where light would no longer be able to escape. Within that sphere, 3.66 miles from edge to edge, is the entire mass of our current sun, packed into a single pinprick’s worth of space, instead of filling 432,700 miles of space.
It’s the same scenario with the black hole produced at the end of a supernova; the black hole hasn’t grown in mass, or expanded its gravitational reach- it’s simply much more dense, so you (or light) can get much closer to the center of the black hole, while still being pulled on by the full mass of the black hole. It’s this combination of proximity and mass concentration that produces the gravitational extremes we’ve come to associate with black holes!
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