Cloud height is commonly used to refer to the height of the cloud base above ground level. (This is what the ceilometer reports.) However, it can also be used to refer to the thickness of a cloud, which is the difference in height between the base and very top of the cloud. It is possible for a ceilometer to estimate the thickness of thinner clouds. Occasionally, when reporting satellite data, it can also be used to refer to the height of the very top of a cloud above ground level.
At any one time, there may be several separate layers of cloud above a point on the ground. Each of these is a cloud layer, and each is given a cloud base height when it is detected by a ceilometer. The WMO (World Meteorological Organization) has set out rules that govern the minimum vertical separation that is required between layers before reporting more than one layer of cloud.
The cloud base is the lowest part of a cloud that passes overhead. It is typically measured with a ceilometer.