Height, altitude, elevation mean the distance a thing rises above the level on which it stands, or the vertical distance between a given level taken as a base and a thing that is above it.
Height may be used with reference to whatever can be so measured, whether high or low by a standard of comparison.
It may be used interchangeably with any of the other words, but it is not so explicit. While altitude and elevation are often interchangeable, altitude may be preferred in referring to vertical distance above the surface of the earth or above sea level or to the vertical distance above the horizon in angular measurement.
Elevation is used especially in reference to vertical height above sea level on the surface of the earth; thus, one would speak of the altitude rather than the elevation of a balloon; a village situated at an elevation, preferable to altitude, of 2000 feet.