What is the difference between a positioning flight and a ferry flight?
A positioning flight is a flight for the sole purpose of positioning the aircraft to conduct another flight from another airport. This is often done when the aircraft finishes its day in one city, but is needed in a different city the following day because another plane has broken down. 

A positioning flight is technically a type of ferry flight, however the latter is a more broad term. Examples of ferry flights include delivery from the manufacturer, or flying to a different city for heavy maintenance. 

Both flights are generally conducted without fare-paying passengers on board, but sometimes extra airline staff are carried.