ImgBurn doesn't use a database. It reports the drive string as reported from the drive.
The 209E, U, and M are all roughly the same drive, just for different markets: they're all the BDR-209M.
The drive reports itself as a 209M thusly.
But! There are different features for some different builds of the different Pioneer drives. Your retail model may have extra features enabled via firmware that a barebones OEM BDR-209M might not have.
Oh, and yes, Pioneer's retail boxes in the U.S. (and some other regions) don't use the model number of the drive directly, but instead use an inventory number which still corresponds to one drive as well as the contents of the box.
So by getting the DVR-1810 a while back, you got a DVR-112 (whichever variant you were promised) and whatever software it came with back then.
Here, the BDR-2209 package includes a BDR-209M drive and whatever software. This is normal.
Check to see if the software on the included disc includes a Pioneer drive utility that can enable or disable a few features.
Or: when you open ImgBurn, for both drives, there should be a firmware version listen, as well as a kernel version right next to it. Tell us if the kernel versions match. For example, if the log line reads something like...
I 17:34:54 -> Drive 1 - Info: PIONEER BD-RW BDR-209M 1.34-ID60 (L:) (RAID)
The firmware version is 1.34, and the kernel type is ID60. Tell us what the kernel version/kernel type is for each drive.