There is no difference between the two on how the label is placed on the vial, or in the size and dimensions or material. The difference is in how the labels are rolled and placed onto the lining. Portrait labels (below) are rolled lengthwise and so the roll will hold fewer labels. But this allows the bar code printer to print from left to right, rather than top to bottom. This produces a much clearer label for scanning.
Landscape labels (below) are printed from top to bottom, making the bar code less clear for scanning if the value bar coded contains letters or is very long. Rolled width-wise, the landscape will use less ribbon and allow for more labels per roll.