The word that describes both of those is diagonal. A square or a rectangle has two equal diagonals.
If you had to differentiate between one diagonal and another you could do so in plain English by saying something like 'upper left to lower right. In mathematical diagrams, the sides or corners of a shape may be labelled and you can refer to those.
Just like the directions you referred to - left, right, up and down - diagonals are relative, unlike compass directions which are absolute.