Waves are disturbances that propagate through space and time. Classically, they travelled through a medium, disturbing the particles but not changing their mean position. Electromagnetic waves/particle-waves need no medium; they are disturbances in their respective fields.
Waves are observable physical phenomena that propagate the movement of energy through space and time. Some waves, like sound, require a material medium to propagate energy; disturbing the matter through which the wave passes. Electromagnetic waves/particle-waves require no medium for propagation; they disturb their own respective fields they generate.