There are 2 main methods to make climbing shoes: slip-last and board-last construction. Slip-lasted shoes are by far the most common today, with only a handful of manufacturers still producing board-lasted shoes.
The rule-of-thumb: Board-last construction creates a relatively stiff, supportive shoe and is reserved for flat, comfort-oriented kicks. Slip-last construction on the other hand can be used to create any style of shoe from a noodle-soft slipper to a morning-wood stiff high-top.
Although a flat and stiff shoe can be either board or slip-lasted, a soft or aggressively downturned shoe is the exclusive realm of slip-last construction.