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 tablespoon is a unit of volume in the US customary system and uses the symbol Tbsp.
In the kitchen, the tablespoon is the larger of the commonly used spoons served at the table and represents 1/2 US fluid ounce or, expressed in SI / metric format; 14.78676 ml.
This is often expressed as equivalent to 3 teaspoons (3 Tsp) although strictly speaking it is a little under the size of 3 metric teaspoons (5 ml) at 4.92892159375 ml. It was established to assist normal kitchens with recipes without the need for specific measuring equipment or devices. Although many spoons differ in sizes (and very rarely is a spoon filled accurately) it allowed for a decent "catch-all" and gave a "good enough" result most of the time.