Debossing makes use of two separate metal dies that come together with the sheet of paper inbetween them. The force of a press sandwiches the paper between these two dies and sculpts the paper with the effect of deep impression into the sheet. The reverse side of the paper will appear embossed while the front will appear debossed, or pressed in.
Blind letterpress uses a single metal die that presses into the surface of the paper on one side. It's called blind letterpress because this process is usually done with ink. Without the ink, all that is left is the impression into the surface of the paper stock.
Debossing is best for shaping larger areas where a greater level of depth is needed. However, the reverse side will be heavily affected.
Blind letterpress is ideal for small details on thicker paper stocks and looks best on soft cotton paper.