I have BD Pole saw and a smaller chain saw.They use the same 18 volt battery.
HPB18-OPE-1. I wonder if this battery will work in one of BD drills. If so which model

I have several 18V BD batteries and several BD tools (Drills, Hedge Trimmer and String Trimmer). The numbers on some of the batteries are HPB18 (no other numbers or letters shown on those). Other batteries that I use interchangeably have a #244760-00 number on them. I believe that the HPB18 batteries most likely came with the tools and the others were purchased as extra batteries only.
One of the drills is model CDC 1800.
I believe that barring any unusual circumstances-- if the battery will fit properly onto the tool-it will work.

Thanks a million