Main Difference
The main difference between Tablespoon and Teaspoon is that the Tablespoon is a kind of spoon and unit of volume and Teaspoon is a kind of spoon.
Tablespoon
A tablespoon is a large spoon used for serving. In many English-speaking regions, the term now refers to a large spoon used for serving, however, in some regions, including parts of Canada, it is the largest type of spoon used for eating.
By extension, the term is also used as a cooking measure of volume. In this capacity, it is most commonly abbreviated tbsp or T, and occasionally referred to as a tablespoonful to distinguish it from the utensil. The unit of measurement varies by region: a United States tablespoon is approximately 14.8 ml (0.50 US fl oz), a United Kingdom and Canadian tablespoon is exactly 15 ml (0.51 US fl oz), and an Australian tablespoon is 20 ml (0.68 US fl oz). The capacity of the utensil (as opposed to the measurement) is not defined by law or custom and bears no particular relation to the measurement.
Teaspoon
A teaspoon is an item of cutlery, a small spoon.
By extension the term ‘teaspoon’ (usually abbreviated tsp.) is used as a cooking measure of volume, of approximately 5 ml.
Tablespoon (noun)
A large spoon, used for eating food from a bowl.
Tablespoon (noun)
A spoon too large for eating, usually used for cooking or serving.
Tablespoon (noun)
A ml; in Britain and Canada: exactly 15 ml; in Australia: four teaspoons or 20 ml.
Teaspoon (noun)
A small spoon used to stir the contents of a cup or glass.
Teaspoon (noun)
A unit of measure, equivalent to one-third of a tablespoon or roughly five milliliters.