Vertical position or vertical location is a position along a vertical direction above or below a given vertical datum (reference level).
Vertical distance or vertical separation is the distance between two vertical positions.
Many vertical coordinates exist for expressing vertical position: depth, height, altitude, elevation, etc.
Points lying on an equigeopotential surface are said to be on the same vertical level, as in a water level.
The International Organization for Standardization (ISO), more specifically ISO 19111, offers the following two definitions:
depth: "distance of a point from a chosen reference surface measured downward along a line perpendicular to that surface."
height: "distance of a point from a chosen reference surface measured upward along a line perpendicular to that surface";
ISO 6709 (2008 version) makes the following additional definition:
altitude: "height where the chosen reference surface is mean sea level"
The International Civil Aviation Organization (ICAO) offers similar definitions:
altitude: "the vertical distance of a level, a point or an object considered as a point, measured from the mean sea level (MSL);"
height: "the vertical distance of a level, a point or an object considered as a point, measured from a specific datum."
ICAO further defines:
elevation': "the vertical distance of a point or a level, on or affixed to the surface of the earth, measured from mean sea level."
I.e., elevation would be the altitude of the ground or a building.
Several physical quantities may be defined based on the definitions above:
Depth below seafloor
Depth in a well
Drying height
Dynamic height
Ellipsoidal height
Geocentric altitude
Geopotential
Heights in geodesy
Height above mean sea level
Height above average terrain
Height above ground level
Measured depth
Normal height
Orthometric height
Thickness (geology)
True vertical depth
Vertical distance quantities, such as orthometric height, may be expressed in various units: metres, feet, etc.