I saw an informative youtube video about this by donnaleigh. Unfortunately, I can´t link to it, but you can easily look it up. Both Snake and Fox are liars, but Fox is putting on a mask or costume, trying to charm and manipulate his way into others giving him what he wants. He makes you think you will win by doing what he says, so the snake in the Garden of Eden is really a Fox. The Wolf in Little Red Riding Hood is a Fox, as are Jack Sparrow and some politicians.
The Snake doesn´t have as much intelligence, or is too aggressive to don a cloak. It lashes out to hurt you, spreads lies about everybody in the office so that nobody believes it anymore, Cinderella´s step-mother is a Snake, saying that Cinderella is too low and dirty to be allowed to try on the glass-slipper. It is more open in it´s attacks, and easier to see through.
Many people go back and forth between being the Snake and Fox, like Scar does in The Lion King. You can practise , when looking at films and reading books, to tell when persons are being Foxes or Snakes. I would say Mr Alfred Jingle in The Pickwick Papers by Charles Dickens is a Fox, and Uriah Heep in David Copperfield by the same author is mostly a Fox but goes back and forth a bit when he is openly triumphant or so angry he cannot control himself he turns into a Snake.