Actually a common misconception but not true. The same parent company owns both as well as Porter Cable and Delta but the parts are different, and made on different lines and factories.
There is a little overlap, the battery case for the new PC cordless is the same as the B&D with a small tab to prevent putting them in the wrong brand, but also the pinout is different and if you open them up the cells that make up the battery packs are different. I was hoping to use the nicer chargers and batteries from my PC drill set with the B&D lawn tools which hang on a simple trickle charger but I'd have to do a lot of rewiring to make it happen even though they look very much the same on the outside and filing off the tabs they will plug in.