The thickness of the fabric and whether or not you press your seams makes a huge difference.
The fabric in the upper picture is so thin you can actually see through it, while the one in the lower picture looks quite thick and almost like felt. Thicker fabric will always create thicker seams.
To create a nice flat seam you basically want the fabric to fold as flat as possible at the very center of the seam. This can only be achieved by pressing / ironing the seams open. Have a look at my fabulous diagram:
When you sew two pieces of fabric together, they lay straight. When you open the seam, both pieces try to stay as straight as possible, creating those "lips". If one piece of fabric is thicker / stronger than the other one, it will stay straight and force the weaker piece to bend.
By pressing / ironing the seam you tell the fabric exactly where to fold in which direction, creating a neat, flat seam. It works so well that you can make a seam in a woven cotton fabric almost invisible.