To make your life simple, one major difference between the two is
A sheath dress is well fitted, like a body con and shows of all the curves of your body. It looks good on Rectangular Body Shape, Tubular Body Shape, Hourglass Body Shape and also on small to medium Triangular Body shape. Sheath dresses are more dressier and can be used for work as well.
A Shift dress is straight fit, loose dress. It flatters all body shapes. They are very casual and work very well in hot humid weather.