Vertical distance measurements in the "down" direction are commonly referred to as depth.
In aviation, the term altitude can have several meanings, and is always qualified by explicitly adding a modifier (e.g. "true altitude"), or implicitly through the context of the communication. Parties exchanging altitude information must be clear which definition is being used.
Aviation altitude is measured using either mean sea level (MSL) or local ground level (above ground level, or AGL) as the reference datum.
Pressure altitude divided by 100 feet (30 m) is the flight level, and is used above the transition altitude (18,000 feet (5,500 m) in the US, but may be as low as 3,000 feet (910 m) in other jurisdictions); so when the altimeter reads 18,000 ft on the standard pressure setting the aircraft is said to be at "Flight level 180". When flying at a flight level, the altimeter is always set to standard pressure (29.92 inHg or 1013.25 hPa).