How are xylem vessels and phloem sieve tubes specialised from cambium?

The vascular cambium is the lateral meristem that forms the secondary vascular tissues.  It is located beyween the xylem and the phloem.  Meristematic cells are undifferentiated.  They carry on cell division indefinitely.  They not only add cells to the plant body, they perpetuate themselves.  Some of the products of cell division in the cambium do not develop into adult cells but remain meristematic.  

Both xylem vessels and phloem sieve tubes are fully differentiated adult cell types incapable of further cell division.  For the specifics of each cell type please see references #2 and #3 below.