I don't know how to call this but how to make a monochrome like the one on bottom. The exclusion (white), but originally it doesn't overlap.
There's no trick or filter to making all-monochrome versions of your logo like this. I guess this designer simply drew the white contours so they would suggest the corresponding shapes in the colour version. Monochromising a logo can be quite an art.
Select all, then choose
Edit > Edit Colors > Convert to Greyscale.
Then select and adjust values for individual areas as needed.
Select the all white areas around the logo, that which is not logo. Then invert that selection and fill with black.
Then add details to taste.