Why is butane in the lighter a liquid yet the butane in the buret is a gas?

This because when it is in the lighter its is not in contact with the outside environment so the  pressure does not act on it or act in very small amount while in buret it is open from the head and thus pressure acts on it and which cause its vapor pressure to increase more than atmospharic pressure and cause it to change state 
This is because if the vapor pressure rise above atmospharic pressure then it reaches to its boiling point and change state to gas thats why in buret due to pressure difference its is in gas state