Higher frequency beams carry more energy (E = hf). In order of lowest frequency to highest, and therefore least destructive to most, we have: radio waves, terahertz, infrared, visible light, ultraviolet, x-rays, gamma rays. That is why x-rays can give you cancer but infrared does not. In free space, wavelength and frequency are trivially related, f = c/lambda, so that higher frequencies are always shorter wavelengths. You only need to talk about one and other is understood.
That being said, the ability of a laser to damage an object depends on many things: the intensity of the laser beam, the spot size to which the beam is focused, and the way in which the specific material responds to the beam (which is frequency dependent).