There is a type of constant current load, once used for street lighting. Going back in time when electric utilities first started providing street lighting, there was a system that wired the luminaires in series instead of parallel. Each luminaire had a transformer wired in series with the hot leg, and the low side was connected to the bulb. Since the bulbs, all identical, were effectively connected in series, the current delivered to the circuit was a constant regardless of the number of bulbs.
Inside the local distribution substation was a special transformer with a spring loaded counterbalanced armature inserted into the transformer core. Its purpose was to provide a constant current to the string of bulbs by sensing any change in the current demand and adjusting the output voltage accordingly. This allowed the utility to add additional lights to the circuit without concern for the wire size and voltage drop, up to the transformer voltage regulating limit.
A constant current load is one which varies its internal resistance to achieve a constant current regardless of the voltage which is being fed to it and therefore the power will vary. In other words, a constant current load would draw approx the same amount of current, despite wide variations in the source voltage or other impedances in the circuit.
A 4-20ma temp. transducer would be a good example of a constant current load. Consider it is designed to deliver 10mA for 100 deg F. As the input voltage varies from 20 to 24 volts, the output might only change by a small %.
Another older example would be an arc lamp that contains an automatic adjustment of the series resistance in order to keep the arc current, and therefore the supply current, constant over a range of line voltages.
Battery chargers can have constant currents, power systems have constant voltage, - theoretically with inner resistance 0 (practically with 5% inner or short Z, in practice you need voltage constanter or regulater, the opposite of power systems are communication systems with constant current for impedance matching with standardized inner resistances for 50, 75, 150, 600 ohms (impedance) and maximum forward power transformation. An impedance can have only resistance but the people say then resistance and not impedance - theoretically not correct but in use. because electric science has 2 views one for low level easy people and one for higher educated academic language, the same difference is by maxwell equations low level is with integral higher level is with differential, same by laplace and or with heaviside parametric equaetions like wjC. heaviside are using low and high level people. but it is higher level but mathematicians are preferring laplace as higher level. and so on.