Desktop (and generally HTPC) cases lay flat/horizontal across a desktop. The motherboard lays parallel to the desktop. Towers stand upright. The motherboard is perpendicular to the desktop.
The four on the left are towers. The two on the right are desktops.
Form-factors pertain to the type of motherboards they will accept.
Mini-ITX - Small. Usually only one or two expansion slots.
Micro-ATX - Average size. Three or four expansion slots.
ATX - Large. Seven or more expansion slots.
-Wolf sends