The teaspoon is a unit of volume in the US customary system and uses the symbol Tsp.
In the kitchen, the teaspoon is the smaller of the commonly used spoons served at the table and represents 1/6 US fluid ounce, 1/48 US cup or, expressed in SI / metric format; 4.92892159375 ml.
A teaspoon is generally considered a cooking measure but is also used in the administration of medicine when in solution form; 5 ml or multiples thereof is the standard amount of liquid medicine across the world.
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.