Is the unit normal vector or the normalized normal vector at a point on a surface the same as "the normal vector" at that same point (and surface)? Does saying, "the normal vector" imply it is normalized? Wolfram Mathworld says:

The normal vector at a point ![enter image description here](https://i.stack.imgur.com/Sw1VO.gif) on a surface is given by

![enter image description here](https://i.stack.imgur.com/UYAgR.gif)

--> If this is the case, why don't people, when referring to a vector at a certain point on a certain surface, just say "the normal vector" instead of "unit normal vector" or "normalized normal vector"