Modulation is when a piece of music moves from one key to another during the course of the piece. An example is in most Sousa marches, where he modulates up a 4th (adds a flat, for those of use who've played a lot of marches) at the trio. Transposition is taking a piece from one key and playing it in a different key. This is especially common in jazz and pop music, so a song can be played in a more comfortable key for the singer.
this is answer based on my reaserch
