These are all simply marketing terms by Smith & Wesson. Yes, M&P means Military & Police, and many of the features noted above have been designed-in. However, Smith's "M&P" semi-autos also have a certain look-and-feel to them that Smith is marketing. You'll notice that the .380 semi-auto "Bodyguard" used to be sold as just the "Bodyguard":
A year or two ago, they updated the Bodyguard to become the "M&P Bodyguard", and the gun now shares some visual features of their other M&P semi-autos, such as the scalloped serrations in the slide and the slight recess/cut along the front two-thirds of the slide:
The "Shield" is just the name of the gun model, like the "Bodyguard". Smith has not given the full size M&Ps a model name, and it's sometimes confusing that some of their guns have model names and some do not. It's nothing more than Chevrolet calling their sedan "Malibu". The Shield is Smith's single stack 9mm intended for the concealed carry market. The Bodyguard is Smith's smaller .380 intended for deeper concealment.
They also sell a revolver called "M&P". Their M&P revolvers are .357/.38 Spl. They used to sell a "Bodyguard" revolver as well...not sure if they still do.