What is the difference between negative and positive liberty?

Both terms were coined by Isaiah Berlin but proposed by different authors: J S Mill and T H Green respectively.
​Simply put, negative liberty is 'freedom from' constraints and positive liberty is the 'freedom to' achieve your goals and live life as you want.
​The main implication of this definition is that negative liberty implies a small government as there are less laws and constraints passed and positive liberty requires a large state which provides a welfare system and other means for people to be able to achieve their goals.