Letterpress printing is a debossing process, meaning the art is pressed into the paper (usually as it applies ink). In the first photo you can see an example of a different, but similar process called embossing, which is the opposite: the art is coming up out of the paper. This is done with a corresponding set of male and female dies on each side of the paper that press together to create the impression. You’ll see a clear reverse image of the design pressed into the back of the paper.
Another option is doing a blind-deboss, which is still a letterpress process, but where we use no ink, but just press the image into the paper. I usually use 5-10% grey ink for this process just to make sure the image/text doesn’t get lost. It still ends up looking like no ink, but the impression looks deeper. See an example of what this looks like in the image below.