Barometric Altitude, aka Standard Pressure Altitude
This is the type of altitude that aircraft usually transmit on Mode-S. It is the altitude of the aircraft as calculated from the ambient air pressure around the aircraft, assuming that the air pressure at sea level is standard pressure (one atmosphere or 29.92 inches of mercury).
The advantage of transmitting a standard pressure altitude is that every aircraft on an air traffic controller's screen is singing from the same hymn sheet, they are all using the same calculation to work from ambient air pressure to altitude. If two aircraft are shown on the radar as being within close proximity horizontally but 2000 feet apart vertically then it is very likely that one of them really is 2000 feet above the other.
The disadvantage with standard pressure altitudes is that they seldom reflect the actual height of the aircraft from the surface of the ground. If the local air pressure is well below one atmosphere then the standard pressure altitude can show a value that is hundreds of feet higher than the aircraft's actual altitude above mean sea level.
Geometric Altitude, aka Indicated Altitude
This is the altitude of the aircraft above mean sea level. The ADS-B specification allows for the transmission of indicated altitudes but I have never seen it happen, and the Mode-S specification only allows the transmission of standard pressure altitudes.
Calculation of the altitude above mean sea level usually starts with the pilot being told by air traffic control the current air pressure setting for the airport that they're flying to. They enter this setting into their altimeter. The altimeter uses this setting and the ambient air pressure from around the aircraft to calculate the aircraft's altitude above mean sea level.
The advantage of using a geometric altitude is that the pilot knows how close they are to the ground and to ground-based obstacles.
The disadvantage for air traffic control is that two pilots can be at the same real world height above the ground but can be showing different altitudes in the cockpit. They would only show the same altitude above sea level if they both had the same pressure settings entered into their altimeters.
Calculating altitude AMSL
Version 2.4 onwards of Virtual Radar Server will try to calculate the altitude above mean sea level by periodically downloading air pressure settings for airports around the world, finding the one closest to each aircraft and then calculating the indicated altitude on the assumption that the air pressure at sea level for the aircraft is likely to be close to the air pressure reported by the airport.
Pilots and air traffic control are normally interested in the aircraft's altitude above mean sea level when the aircraft is close to the ground and the pilot would like to avoid obstacles.
Once the aircraft gains sufficient altitude to be well clear of any ground-based obstacles the altitude above sea level becomes less interesting. The obstacles that need to be avoided now are other aircraft, and avoiding them gets easier if every aircraft transmits a standard pressure altitude.
Pilots will usually use geometric altitudes up to a certain altitude called the transition altitude. The transition altitude can vary from one air traffic control regime to another.
Above the transition altitude pilots switch over to a standard pressure altitude, but rather than report it as a height in feet (which could be confused with a geometric altitude) they report it as a flight level. Flight levels are the standard pressure altitude divided by 100 feet, so a standard pressure altitude of 30,000 feet is flight level 300 (or FL300), and similarly a flight level of FL271 corresponds to a standard pressure altitude of 27,100 feet.
Virtual Radar Server (from version 2.4 onwards) always reports geometric altitudes below the transition altitude and flight levels based on standard pressure altitudes above the transition altitude.