I think that this is a good question, and central to a lot of the confusion that stems from a casual reading of some modern topics in physics. It's the difference between a black hole in nature, which formed in a realistic process, and the Schwarzschild metric, which has a uniform sphere of "dust" collapsing from infinity, in an empty universe, without gravity, and no angular momentum or charge.

The reason these models are used is because they can give insights and/or generate new tools to explore reality with. On the other hand, they're just maps, just approximations of systems which we couldn't hope to accurately model with fidelity.

On one hand, you get some amazing insights when your models intersect with observations, but you also need to remember... "The map is not the territory."