Difference between Euclidean and Manhattan distance

Euclidean Distance: Euclidean distance is calculated as the square root of the sum of the squared differences between a new point (x) and an existing point (y).

• The Euclidean distance or Euclidean metric is the "ordinary" (i.e.straight-line) distance between two points in Euclidean space.
• The Euclidean distance between points p and q is the length of the line segment connecting them.  

Manhattan Distance: This is the distance between real vectors using the sum of their absolute difference.

• It is the sum of the lengths of the projections of the line segment between the points onto the coordinate axes.