How to stitch together two fabric pieces without creating "lips"
The first one is a machine technique known as flat lock stitching. A machine stitch found on a home sewer that could be used as an alternative would be the three part zigzag. 
Many of the hand stitching techniques are being lost due to the speed of the machine stitches. 

Stoating is a technique I have read about and is very challenging to do by hand.
Here is a link that might be of some interest on stoating: 
https://books.google.com/books?id=k15YAAAAYAAJ&amp;pg=PA343#v=onepage&amp;q&amp;f=true