**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.

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