Here is my breakdown:
There are 2 basic styles of wax: one you remove with strips and one you peel off. In the UK, the one you peel off can be referred to as 'Hot Wax or Film Wax'. Both styles come in cold, warm and hot temperatures. Any wax presented in a roll on is going to be the kind you remove with strips.
I like to keep the definations down to 2 exactly:
Hard Wax - the kind you peel off
Soft Wax - the kind you put on thin and remove with strips.
My preference is to use Hard Wax on Face, Underarms, Bikini/Brazilians. I think this style of wax is stronger, removes hair better and does not stick to the skin, making it best for delicate areas.
Soft Wax is for Arms, Legs, Back and Chest. Can be applied very thin to large areas and removed with strips.
No matter the style or brand, they all remove hair from the root, you just have to learn how to master the brand of your choice. Certainly there are differences from label to label, but they all work.