The height of tower of a lighthouse is (like each other building) the height
of top above the surface. Things like aerials and lightning conductors are in general not included.
The following picture shows an (arbitrary) selection of lighthouses in comparision. All lighthouses are shown in the same scale (1 pixel = 50 cm) and on this way they are easy to compare. The lines mark a distance of 10 metres.
The height of fire is the distance between the sea level and the source of light.
This height depends on the height of the tower and on the location (height) of the lighthouse.
The sea level is defined at the Baltic sea as the mean sea level and at the North sea as the mean high tide. That means, that the true height of fire is mostly (unless flood) higher than the defined height of fire.
The following picture compares different lighthouses and uses the same scale like the picture above.