"In electronics, a constant current system is one that varies the voltage across a load to maintain a constant electric current."
in which way is a lab PSU in CC mode doing anything different?
With a Lab/Bench PSU, if the load drops, the PSU will come out of Current Limit mode.
A CC PSU will not change the current no matter how low the load goes, this is why Lab/Bench PSU are NOT (striclty) CC PSU.
They can be used in a way which can control the current to a fixed level but it is highly dependent on the load.
a true CC PSU has a maximum voltage that it can deliver
Agreed
a true CC PSU has a maximum voltage that it can deliver, I still see no difference. Checked the Keithley's spec out of curiosity: voltage limit is adjustable from 0.1V to 105V. What would it do when that is reached? I presume it will keep the voltage constant at this value.
A CC PSU goes the other way round, if the load resistance goes too high, the PSU may not be able to maintain the current and will hit a Voltage Limit.
The difference is that they have a primary function - Lab/Bench PSU are designed to mainly control voltage and have a secondary function to limit current.
CC PSU are mainly to supply a fixed (maybe adjustable) amount of current no matter the load but are subject to a Voltage Limit/Ceiling.