Basically, they have the same meaning when used as a verb: "Stitch" is more often used in medicine as Anne has mentioned, but it can also be used for an item of clothing. "Sew" can also be used for medicine purposes, but it is more often used for an article of clothing. "Seam" is essentially used for knitting. However, as a noun, the meaning is slightly different: "Stitch" is a style of knitting. "Sewing", which is the noun, is the activity itself of knitting. "Seam" as a noun is what joins two parts of an item of clothing. On trousers, for example, this is between both legs. Does that make sense?

Sewing is the craft of joining objects together with stitches using thread or yarn and a needle while stitching is the process of looping yarn or thread to join two objects together. Seams are rows of stitches which fasten two objects together.

What i know is stitch is the word used in medical term when you got a wound needed to be closed. We don't use sew or seam for this kind of situation. I'll catch up with more upcoming answers.