Are black holes formed when large stars collapse?
When a large star's core runs of of fusible material, the core is mainly iron. Fusion reactions involving iron require more energy than is produced so fusion reactions in the core stop.
Once fusion reactions stop the core starts to collapse under gravity. If the core is more than a few solar masses, nothing can stop the collapse due to gravity.
The Schwarzschild radius
Once the stellar core collapses to its Schwarzschild radius it become a black hole.
There are considered to be three types of black hole. Primordial black holes were created soon after the big bang. Stellar black holes are formed from the collapse of large stars. Supermassive black holes reside at the centres of most galaxies.
So, the relationship between stars and black holes is that stellar black holes are what remains when a large star's core collapses.