It doesn’t help that, by the power of marketing, people can mean multiple distinctly different things when they say “bed leveling”.

What you’re referring to is Z offset. This is the difference between where the endstop or probe triggers versus the actual Z coordinate of the nozzle. This is generally what you’re trying to set with the paper test. The paper test is only mostly accurate, though. A set of feeler gauges will do the same job with better accuracy.

It can also mean tramming, which is making the bed itself planar to the printer’s gantry. This is what you’re doing when you adjust the ‘bed leveling’ screws on a printer or what happens automatically if you have triple lead ‘bed leveling.’ It pretty critical that Z offset is set correctly for autotramming. Manual tramming is essentially setting Z offset to be consistent at each of the bed adjustment points.

Finally, mesh compensation also gets called bed leveling. Even if you have a perfectly trammed bed, the reality is that real, physical things (like beds) are never perfectly flat. Mesh compenstation probes multiple points along the bed, registers the difference between Z0 and the probed point, and builds a mesh that the printer uses to compensate for variations in the bed surface. The denser the mesh, the better the printer can compensate for small variations in surface flatness.

All of these things are complementary and will have an impact on each other. The fact that they all get lumped into “bed leveling” causes a lot of confusion for folks when understanding what each is and does is pretty important to get the most out of a printer.