There is a question already dealing with the difference between elevation and altitude: Which to use: "altitude" or "elevation" in regards to height above sea level?
The difference between the terms is clear, from the first answer I quote:
"Altitude is typically only used to describe the height of an aircraft in flight. It is a barometric measurement expressed relative to the height of a runway or mean sea level in a given location or region (taking into account current local atmospheric conditions), or to an arbitrary standard datum (to eliminate the effect of localised variations in air pressure).
Elevation is usually used to describe the height of the ground, or a feature fixed to the ground. It is a geometric measurement expressed relative to the mean sea level datum established for the region by the national mapping agency."
So a church somewhere in the landscape has a certain elevation and when I fly with my balloon to New Mexico I would use the term altitude. Also atmospheric pressure decreases with altitude.
The situation however, is less clear cut when I talk about the weather up in the mountains. Should I say "it is -12 °C at 2000 meters of elevation" or should I rather use the term altitude here? Temperature is measured by a weather station with a sensor positioned on a post above the ground level. I tend to think that I should refer to temperature as being related to elevation as here, the atmosphere is so close to the land surface. But what is correct?