(for various reasons I needed to join a mismatched pair of 18v drill and battery, annoyed at how much fun it was)
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The pinout on the orange B&D is exactly the same as PC 20v, and there's only like two little nubbins of plastic on the battery case, and two tabs on the PC tools that make them physically incompatible. I use them interchangeably after some dremel engineering (that gets nowhere near the electricals). Same as those now-retired Bostitch 18v, and I understand non-US "fat max" batteries and a certain limited line of 20v craftsman stuff from a decade ago is also the "same."
The newer Craftsman that S-B&D makes looks to have been designed along similar lines, but they flipped + and - and added enough plastic-work that I think it'd be non-trivial to hack them up. I haven't investigated to see whether, electrically speaking, they are more B&D or more DeWalt.
That's something I really don't like, is...there can be engineering reasons for those lockout nubbins to be there. My Craftsman V20 chargers have two lights on them, one labelled "V20" and another labeled "V12". Which suggests there were plans to make 12 volt batteries in this form factor, I guess for a "Flex Volt But Worse" idea that never emerged. Some tools might be 20V only or 12V only and you would NEED to prevent them from interchanging or else you'll let out the magic smoke. Or in the case where the pinouts are different for some reason.
And sometimes the marketing department put them there so that most of the population will think they need to buy more batteries when there's no technical reason for them to do that. Which is why I have a bit of a problem in general with one company selling interchangeable products under multiple different brands. But that's a whole other bag of cats.
I also haven't really got a lot of hands on time with DeWalt's 20 Volt tools or batteries, I do know that some of the Brushless Craftsman tools bear strong family resemblance to DeWalt's line, so I imagine the same engineering firm is designing tools for both.