What is the different between an increase in demand and an extension in demand?

First of all this is something that people very frequently struggle with and it can be difficult to get your head around at first. But if we were to look at the demand curve it is easier to visualise the difference. An extension of demand can be seen as a movement along the demand curve. This movement would be caused by a change in the price of the product in question.
An increase in demand can be seen as a rightward shift of the demand curve. This shift can be caused by a number of factors. For example a shift in demand for a product because of a change in the price of a substitute good. This could be when the price of Chicken increases, we will see a rightward shift, increase in the demand for turkey.