How can I generate different categories in sidebar left and sidebar right as in your wallpress live demo

Hi Christian, 
The “Clothes, Jackets, T-Shirts, Accessories”: they are categories from Jigoshop.
You can create them in the product categories in the Jigoshop > Categories.
After that, you can go to Appearance > Widgets >  Jigoshop: Product categories widget, then add this plugin to the Sidebar shop.
See the screenshot:

Categories: Sport, Fashion Hight-tech, Entertainement: they are post categories.
To add these Categories: log in to Dashboard > Posts > Categories > Add new
Then go to Appearance > Widgets > Use Custom Menu widget add to the Secondary Sidebar.
See the screenshot: 

Hope this helps!