So the reason for the gap with KASP is because those are more like props rather than environments. It's basically a flat plane running parallel above the floor. Depending on what you're trying to accomplish, HDRI is probably a better option. It's important to find the right HDRI for the right situation as well.
Looking at the first example again, it looks like you might be applying the HDRI as a backdrop instead of environment map. HDRIs are meant to wrap around the scene like a present with your assets on the inside.
Rather than applying the HDRI to the environment pane as a backdrop, find it in your content list and just double-click the one you want to apply to the scene. What may be misleading you is that when you do this, you won't see it in the viewport like you do with backdrop. You can turn on your IRAY preview to see it.
See examples below both using Sedor Iray Sky 34.
HDRI as backdrop:
HDRI as environment map: