Lasers are a focused light energy beam that are wavelenght specific for their intended purpose.
Nd-Yag is wavelength specific to treat diseased tissue to ablate only the diseased tissue leaving the healthy tissue and santizes the pocket giving the tissue a significant chance to heal without making an incision. This reduces the healing complications to very minimal and the time is also greatly reduced. This can be used if the periodontal disease has been caught and treated in an early enough stage. This treats the specific tissue and not all the tissue with heat generated at tip on some other less desirable wavelenghts that heats all tissue, and then the healthy tissue also being heated to the point of requiring healing time and possible post treatment complications including pain.
Er-Yag is a wavelength specific to make incision with significantly reduce bleeding and reduced healing time, and also to prepare for fillings without numbing in select cases, e.g. teeth without metal fillings existing.
Laser is a general term to describe the focusing of light energy to a beam of energy. They can vary from the pocket pointer with visible red beam to the metal cutiing beam. Each wavelength has specific properties that are used for specific intentions, and one wavelength can not do everything.
Er-Yag is similar the wavelength used in opthamology.