Sounds and waves (wav) are files that contain a digitised version of the sound itself so they just need putting through a digital to analogue converter then playing back through headphones or loudspeakers.
However MIDI files contain instructions to tell a synthesiser or sound module what notes to play. You can think of them as being like the old fashion player-piano with a roll of paper with holes punched in it that makes the keys move as the holes pass under a special mechanism. However MIDI files can tell the sound module what sounds to play as well as many other things to control the sound.
hope that helps
SysEx.