How would you go about creating this type of motion graphics - cloth simulations?

I’m looking to create some things such as these:

But I had some trouble today when trying to create something similar. Personally, I tried having a plane act as a cloth and have it drop on another plane with cloud displacement on it, and animate the displacement so that it would move the cloth that’s on top, creating these movements. I got what I expected I’d get from such a workflow, but it doesn’t quite look like what you see in those 2 links.

Any advice on this?

You can add weight paint to the cloth/plane… to help control where it will billow…
quick example frame…