The difference is in the detail of the roofline and upstairs windows. If the house has dormers (windows with living space that juts out from the roofline) or gables with windows then by definition it is a 1 1/2-storey. Another way to describe it is if there is a loft or living space between the roofline and top of the first floor, then it's a 1 1/2-storey.
A 2-storey home will typically have consistent 8 or 9 foot ceilings throughout, with hardly an area dipping below that ceiling height. The living space on the second level of a 1 1/2-storey can instead find many sloped ceilings and reaching low wall heights of a few feet, or less. Another way to describe a 1 1/2-storey is to imagine the living area as being "inside" the attic space of the roof.