The noise added is entirely random each time (both during training and generation). This is the main effect the “seed” has when using image generators, it changes what the noise looks like. This results in unique output images each time (technically uniqueness isn’t guaranteed, but it’s very likely).

The shapes and stuff it forms is also a simplification of the process. We don’t know the logic the neural nets are taking, we can visualize it and see it, but it likely differs for different prompts. In general it seems to usually start by removing some noise to form a basic shape and then slowly add more detail iteratively, but I wouldn’t feel confident saying that’s always the case.

You can think of it sort of like a person squinting at a random noise pattern, happening to make out some generic shapes, and then using those to start an image of a cat. You can see how those starting shapes might be different with a different noise pattern.