The product of [tex](m - n)^{2}[/tex] is different because it is the squared of (m - n), meaning that it multiplies by itself which equates to [tex]m^2 - 2mn + n^2[/tex]. The other one represent the special products which equals to [tex]m^2 - n^2[/tex].
The correct product of (4a - 2b) and (4a + 2b) is [tex]16a^2 - 4b^2[/tex].