Black homes are so massive and heavy that they bend light (well, technically every piece of mass does, even yo momma). It's bend so extreme that that accretion disk appears warped.

A similar thing happens with neutron stars that can also bend light in such a way that you can actually see part of the back of the star (if you were able to see it anyway, it would be dark) as light that would be emitted from parts of the back would warp around to the front where you could see it

Yep, you got it right. The accretion disk is actually really flat. Those images are produced in simulations that take into account the curved (and very complex) paths light takes in the vicinity of a black hole. These images really depend on the angle between the line of sight and the disk.

Or is it exactly like saturns rings but we see the whole ring bent round the top because a black hole bends the light around so we can see it?

Hit the nail pretty hard on the head there

The second one. The image is simulated as how an external observer would see it. It was firstly done for the Interstellar movie.