Would you use sew when it talks about wound?
I hear some people using stitching while they talked about trousers and clothes.
OK. A "stitch" is a single loop of thread, used to bind pieces of fabric (or other material) together, as when one uses a needle to draw a thread through the fabric layers. "Stitch" is countable (though different people may have different ways to count what is a stitch, especially for more complex ones, like an overlock stitch).
"Stitching", then is making repeated stitches, whether to bind up a wound or to put together a garment. (Or make a quilt, etc.)
"Sewing" is the activity involved in making items out of fabric or similar materials, using techniques resembling stitching. (What a "technique resembling stitching" means is subject to individual interpretation, but might include gluing, fastening together with rivets, fusing with heat, etc.) "Sew" is a verb (where "stitch" is both a noun and a verb), though "sewing" can be used as an uncountable noun.
Sewn items might be articles of clothing, curtains, coverings for pieces of furniture, bedding, the "convertible" roof of a car, or a dozen other things.
Either term may be used in a metaphorical sense -- "stitch together an alliance", "sew up a business deal".
In modern English, "to sew" and "to stitch" are roughly interchangeable. There is a slight difference in meaning, but the most important factor that will dictate your usage is the context: what word does your audience expect to hear?
First, note the somewhat circular definitions of the two words.
I guess because the verb forms are slightly different, which word you use will also depend on your sentence structure (whether or not you have a direct object).
Second, the words have different origins but have converged in meaning over time.
Old English siwian "to stitch, sew, mend, patch, knit together," earlier siowian, from Proto-Germanic *siwjanan (cognates: Old Norse syja, Swedish sy, Danish sye, Old Frisian sia, Old High German siuwan, Gothic siujan "to sew"), from PIE [Proto-Indo-European] root *syu- "to bind, sew" (cognates: . . .
And it lists approximately 92,000 cognates: "sew" is an old word that was quite popular in many languages. "Stitch" is likely as old, but it seems to have lacked panache: it was not as popular and starting in the 13th century in English, the original sense of the word, "to stab", dwindled and stitch became part of the lexicon of sewing and binding.
Old English stice "a prick, puncture, sting, stab," from Proto-Germanic *stikiz (cognates: Old Frisian steke, Old High German stih, German Stich "a pricking, prick, sting, stab"), from PIE *stig-i-, from root *steig- "to stick; pointed" (see stick (v.)). The sense of "sudden, stabbing pain in the side" was in late Old English.
Senses in sewing and shoemaking first recorded late 13c. . . Surgical sense first recorded 1520s.
stitch (v.) c.1200, "to stab, pierce," also "to fasten or adorn with stitches;"
Technically, as verbs, you probably cannot interchange sew and stitch without modifying your sentence, but the meaning of the action will almost certainly be clear to your audience whichever word you use. Your word choice will largely be based on convention or what your audience expects to hear.
According to this thread, sewing implies something being created while stitching implies repair.
Another connotation that I think exists is that a stitch refers to attaching a string onto fabric, while sewing (I think) implies making that fabric beforehand? If you go on google images and type in stitching you will see various patterns of attaching string onto an already existing fabric.
For medical purposes, you always stitch up a wound, or suture it. When a doctor stitches your wound you have stitches. Another meaning of stitch is the lovable Disney character, who was named (from we know) arbitrarily by Lilo.