In basic terms a box rule provided min and or max values for certain parameters.

A formula rule allows flexibility of certain chosen parameters such that the end combination or formula ends up being equal. For example you may increase length if some corresponding reduction in width is taken into account. In a formula rule class it is possible for a 16 foot boat to race equal to an 18 provided both meet the formula.

Within either case there can be any number of restrictions for things like build materials or any number of measurements required. An A class is technically a box rule with relatively few restrictions. An F18 is also a box rule with a lot of restrictions.

There is a little bit of gray area in the F16 and F18, where the sea lawyers could make their pay, involved with the sail size and plan being changeable with weight or crew respectively. My take is these are fixed values, so still not Formula per say.