Electromagnetic (EM) waves and matter waves differ primarily in their behavior and fundamental nature. EM waves travel at a constant speed relative to the observer, while mechanical waves, such as those in a string, travel at a constant speed relative to their medium. Matter waves, as described by de Broglie, have extremely small wavelengths for massive objects, highlighting their quantum nature. EM waves are considered more fundamental, as mechanical waves emerge from interactions among large numbers of atoms. Understanding these distinctions is crucial in the study of wave phenomena in physics.