There is sort-of a philosophical difference between "current limiting" and "constant current" (or "controlled current").
Current limiting is typically used in place of a fuse so if you short or overload your power supply it temporarily shuts-down or the voltage "folds back" to protect the power supply.
Constant current/controlled current is typically used to drive LEDs with a known-current. If you disconnect the load from a constant-current power supply the voltage jumps-up to its maximum as it tries to push current through infinite resistance.
Some bench/lab power supplies have an adjustable current limit so they can be used as a variable current source but it's mainly to protect the circuit (and to protect the power supply when set to maximum).
If you want to dim a regular incandescent light bulb you typically reduce the DC voltage, "PWM" the DC voltage, or "chop" the AC waveform.
If you want to dim an LED you can use PWM or you can use a controlled current power supply.