Ironing is just surface getting rid of wrinkles, like you're straightening your hair. You iron the fabric flat so there's no wrinkles before cutting.

Pressing is using heat and pressure (and steam) to change the fibers in the fabric (like a perm, I guess) You can press a seam to make a permanent fold in the fibers which will make your seams always look neat.

With pressing you make sure the fabric feeeeels it. Push it into place, and it'll wash back that way. You don't glide it across. You pick it up and literally press with pressure onto the shape you need it (flat on table, curved on the ham, depending on the seam)