No, on that graph, it shows variation of delta with moneyness,ie., how much "in the money" or "out the money" the option is in. So, the more ITM a call option is, the more positive its delta and more ITM a put is, the more negative its delta. Now as underlying value falls, call option becomes more OTM and its delta falls. But at the same time, put option becomes more ITM and so its delta becomes more negative, hence even the put delta reduces.What is moneyless? Stock price - strike price. strike price is constant. In John the graph is captioned "variation of delta with stock price for a call option and a put option on a non dividend paying stock".