Whaddya know! A question for a (former) textile designer like me to answer!
Yes, the fabric is probably printed on one side and the garment is constructed with the printed side inside. Since you can see the printed image on the nonprinted side, but it is fainter, it is probably done with the process called wet printing using a dye that chemically bonds with the fiber. When printed on a thickish fabric, like a tee shirt knit, the dye, which is pressed through a screen, doesn’t make contact with all of the fibers on the underside. That’s why the image is there, but fainter. The feel or “hand” of the fabric isn’t usually affected.
The fabric for the polo shirt was probably printed with a pigment printing method, since its a pale motif on a dark background. The dye is opaque and is attached to the top of the fibers on the printed side, like paint on a wall, so it doesn’t show through to the other side much. Pigment printing is a less expensive process (or used to be) but the quality has improved in the past few decades so that the hand of the fabric is still soft.
I used to hand paint the original concepts for prints for swimwear fabric. Any more questions, anybody?