The Vulkan API does not change between Intel, AMD, NVidia and MoltenVK (iOS/macos) GPUs.

What the grandparent is saying though is "that differences between AMD and nVidia GPUs are exposed." Vulkan is so low-level that your application needs to implement workarounds for each GPU's quirks.

OpenGL was high level enough that if you didn't care too much about raw speed, the only place you got into the weeds of GPU quirks was writing your shaders. With Vulkan, the weeds of GPU quirks pop up everywhere.