The difference between White Core and Black Core is simply the color of the 'beveled edge' of the mat (see images below).
!! Black Core mats are only available in two surface colors. White and Black. White mat with a black core is shown below.
1) Shown here: a Black Mat with a 'White Core' (the beveled edge is a bright white color)
2) Shown here: a White Mat with a 'Black Core' option (the beveled edge is black in color)