OK, so it's going to be more than a word....
There is a difference between ironing and pressing. You iron clothes. Ironing is moving the iron to and fro across the fabric to straighten it. You can iron fabric when you are prepping it for cutting. Once you start piecing, you press. Pressing is an up/down motion. There is no dragging because any dragging could distort your pieces.
If you watch quilting shows, you will hear them say to set the seam before pressing. Setting the seam is taking the fabric as it has been sewn together to the ironing station and pressing it. This takes out any ripples that may have occurred during sewing. Then flip up one layer and press. Whatever direction you want to press the seam, that fabric goes on top and is flipped over. So to press toward the dark fabric, set the seam with the dark fabric on top and flip that fabric up to finish pressing. The seam allowance will be directed toward that dark fabric.
In this picture from Sew Delicious, the seam is being pressed toward the gray fabric.
Some patterns require you to press the seams open. This is done because you have so many seam coming together that the bulk would be too much. Unless the pattern says otherwise, you will want to press your seams to one side or the other.
Some people give another shot of starch when pressing pieces together. Others just use a good dose of steam. Experiment and see what works for you.