What is the differences of ADS-B and geometric height?
ADS-B, and the older Transponder Mode C, report pressure altitude. That is static pressure where the plane is expressed as altitude at which that pressure occurs in international standard atmosphere.

In low pressure area, the same pressure density corresponds occurs at lower geometric altitude with similar difference at all altitudes. In higher temperature, the air is denser and the isobars closer together, so the same pressure altitude occurs at lower geometric altitude and the difference increases with altitude.

However for purpose of traffic separation, pressure altitude is always used. Due to physical properties of air, the pressure always decreases with altitude and at the same altitude changes only slowly with position, so we can always rely on close aircraft observing sufficiently different pressure altitude being at sufficiently different geometrical altitude.

The reason is that while barometric altimeter is simple, accurate to less than 100 ft and every aircraft has it since the early days of aviation, there was no way to measure geometric altitude before selective availability was turned off in GPS in 2000.

Geometrical altitude is altitude above the reference geoid (usually WGS84), a.k.a the sea level. It is only used internally in EGPWS where it is provided by GPS.

In contrast height is in aviation always used to mean height above terrain. It may be measured directly using radar altimeter or it can be estimated from pressure altitude by correcting for sea-level pressure at the nearest airfield.

Radar altitude is used in GPWS as a backup datum and in older such systems  from before GPS was available (those systems could warn if you were too low, but not if you were approaching high ground, because the radar altimeter only measures down while the new GPS-based systems have a terrain map and compare the GPS position with it) and is shown to pilot for reference, but it is not broadcast anywhere.

Approaches are normally flown in reference to the barometric altitude that is corrected for pressure at airport (the altimeter has setting for reference sea-level pressure, QNH), but not temperature. So the barometric altimeter shows true altitude at the airport, but when it's cold, it shows more than true altitude above. That's why some approaches have minimum temperature.

However, both Mode C and ADS-B broadcast pressure altitude, i.e. as calculated for standard pressure of 29.92 inHg/1013 hPa.