You're approaching the subject wrong. Whether a seam lies on the inside or outside of a garment has nothing to do with the type of stitch you use. It's called "inner seam" and "outer seam" respectively and the same stitch can produce an inner and outer seam.
Let's start with this example:
The straight seams are "overlocked" or "serged". This is a method designed to keep fabric edges from fraying and you'll find this type of seam finishing in most industrially sewn clothes. Usually the overlocked edge is on the inside of the garment. Putting it on the outside in this example was a design choice.
There are special sewing machines called "serger" and "overlocker" that sew only this type of seam, but you can also do it on a regular sewing machine using a zig-zag stitch.
This is not a type of stitch. It's the method how most textile items are sewn. You sew them inside out (by putting the fabric "right sides together"), then you finish the edges to avoid fraying and finally you turn the item right side out. That makes the seams very neat and hidden inside the item.
There are many, many ways to sew this type of seam. To give you some names to work with, see this example (click the link to get a short description of every seam type shown below):
What you call "side by side stitching" is not done with fabric, for 2 reasons: fabric is too soft to hold its shape like this and the edges would fray and rip apart. This type of stitching is only done with materials that don't fray (like leather or neoprene) and that cannot fold over like fabric. This particular example is called "cross saddle stitch".