The cup is a unit of volume in the US customary unit system with the symbol cup.
It is equal to 1/2 US customary pint, 1/4 US customary quart and 1/16 US customary gallon. it is also equal to 236.5882365 millilitres.
Used primarily for cooking - the cup was adopted and established as a recognised unit of measure as it could be used by almost anyone in any kitchen. Due to the slight variants in design and size, it is rarely used as an accurate measure for important or critical materials, however it does represent a specific amount and can be used across many recipes to indicate what is needed.
The cubic yard is a unit of volume derived from the imperial system of units. It uses the symbol yd³.
It equals the volume of a cube with edges that each measure 1 yard. It is equivalent to 27 ft³, 46656 in³ or ≈ 0.764554 m³.
The yard (and derivatives like the cubic yard for example) are the same in both the imperial systems and US customary systems so require less conversion systems to calculate / convert to SI or metric.