I've looked them up in several dictionaries, but I find them very similar in meaning because both mean to turn something around something else, for example: She wound a scarf around her neck. She wrapped a scarf around her neck.
I suppose native speakers would answer better, but according to Cambridge dictionary, wrap doesn't necessarily mean around. You can cover something with a piece of material in order to "wrap" it.
But wind implies that something turns, so if you "wind" a scarf, you wind it around a neck. You can't just lay down the scarf on the neck and say you've wound it.
You wrap a package with or in paper.
You can wrap an object with any type of material like paper or cloth or even chocolate. It means to surround the object completely with the material.
Wind is different: wind means that a string or steel cable or thread (or anything like that, a filament) is put around and around some object. Winding means has been placed around something round and is circular in motion. Wrapping envelops an object.
Thread is wound (wind, wound, wound) on a spool.
Spools are have thread or filaments wound around them.
wind and winding is used a lot with images:
- to wind someone around your finger [get them to do what you want]
- to wind someone up [BrE, to make them believe something that is not true]
- roads are said to wind through places.
- Song: Long and Winding Road
If something like a road winds through a landscape, it is not straight. It has curves in it.
Well, that's the short of it but probably not the long of it. [idiom: the short and long of something]
She wound the scarf around her neck means the neck is like the spool and the scarf is like the thread. For this, the scarf must be long and thin. A short scarf would not work here.
She wrapped the scarf around her neck means she enveloped her neck with the scarf, like a package is wrapped with paper.