Illustration like [this](https://i.stack.imgur.com/B5szS.jpg) are a way where you try to use 3D to show the curvature 2D area of space. It is a bit if you illustrate the shape of the earth with just a circle, not a sphere.
Images like https://en.wikipedia.org/wiki/File:Black_hole_-_Messier_87_crop_max_res.jpg have the black hole in the middle. What is seen is the accretion disk of matter that orbit the black hole. You can compare it to the rings around Jupiter.
The accretion disk is a disk because if stuff orbited in all directions there would be lots of collisions. It is the collision and other interactions that result in that it ends up in a single disc. There is not a lot of difference in the orbital plane of planes in our solar system for the
Even if you look at the Accretion disk from the side you will see a dark center with light around it. The reason is black holes bend light so that you can see the accretion disk behind the black hole, the light have bend around.
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