Yes, if you reduce the current through an LED, it gets dimmer. The quantum nature of semiconductor junctions means the wavelength stays the same[1], unlike tungsten.
However, since LEDs are very non-linear in their brightness to current curve, LED lamps that provide a dimming function tend to do so by flashing on and off at high frequency, varying the ratio between on time and off time. This is more power efficient, and can be done by simple digital circuitry.
My bugbear is that this PWM dimming is nearly always done at too low a frequency. 100-1000Hz is typical, which means you can see the flashing as soon as there's any motion (eg, car taillights become strings of dots), it tends to cause eyestrain when you try to read by it, and it makes life hell for people with photosensitive migraine, autism spectrum conditions, and some kinds of visual impairment. Ideally, the PWM frequency should be well above the audio band, so as not to cause problems with whistling inductors.
[1] At least for a pure monochromatic LED. White and some other colours are produced by phosphors, and are a bit more complicated.