That’s right, all it is is an auto-copy program. It doesn’t host a shared folder like NextCloud; it just saves you the clicks (or commands) of copying your newly-changed files to all the places you want a copy to be.

If you edit a file on your machine, and your wife edits her copy, you might even find there to be a conflict. (I don’t use Syncthing so I don’t know how it handles this)