Help with pulling category and sub-categories

I need to pull a list of categories and the sub-categories within each one. What I don’t want is a list of the posts within those categories like “loop” does. And I need it more specific than just a list of links like some of the built in functions.

I will do my best to illustrate what I’m looking for here:

//////////////////////////////////////////////////////

Category Name (doesn’t need to link)

Sub-Category
– Sub-sub-category (link)
– Sub-sub-category (link)
– Sub-sub-category (link)
– Sub-sub-category (link)

Sub-Category
– Sub-sub-category (link)
– Sub-sub-category (link)
– Sub-sub-category (link)
– Sub-sub-category (link)

//////////////////////////////////////////////////////

Category Name (doesn’t need to link)

Sub-Category
– Sub-sub-category (link)
– Sub-sub-category (link)
– Sub-sub-category (link)
– Sub-sub-category (link)

Sub-Category
– Sub-sub-category (link)
– Sub-sub-category (link)
– Sub-sub-category (link)
– Sub-sub-category (link)

//////////////////////////////////////////////////////

*** PLEASE NOTE: the links for the sub-sub-category needs to link to a more typical category type page that will list the specific posts for that sub-sub-category ***

I’m misunderstanding some of the syntax of how to do this. I’ve tried a number of options from examples on here or online resources, but I can only seem to pull the posts, rather than lists of the categories and sub-categories that I can format the design and style of.

I hope this makes sense and any guidance would be GREATLY appreciated.