The square knot and the granny knot are two of the most commonly confused knots in basic rope work. Both are binding knots formed by tying two simple crossings of two rope ends. The critical difference: in the square knot, the two crossings are MIRROR IMAGES of each other (left-over-right, then right-over-left). In the granny knot, both crossings go the same way (left-over-right, then left-over-right). This tiny difference completely changes the knot's behaviour.
The square knot (also called "reef knot" in sailing tradition) holds securely as a binding knot — wrapping a package, tying a bandana, securing a coil of rope, or any application where two ends of rope are tied around something. Under tension it sits stable and secure. The granny knot, by contrast, slips and capsizes under tension. It looks similar but cannot be trusted for any load-bearing application.
Neither knot should be used for joining two ropes in climbing applications. Both are too prone to slipping for any safety-critical use. The double fisherman's knot is the standard for joining ropes; the figure-8 follow-through is the standard for tie-ins. The square-vs-granny distinction matters for camping, sailing, scouting, and basic rope work — not for climbing safety.