W&W placed their model 12 on the market in 1887. The D-12 followed in 1890. I do not know what change resulted in the D-12 designation. Just as a guess, that 1889 patent covered whatever made it a D-12.
Singer bought the W&W company in 1905 & continued making several of the W&W models. So far as I am aware of All Singer machines which were built in the W&W plant had the W in their model designation. All machines were not marked with their model on the machine itself. For a period of time, these W&W machines made by Singer continued to carry W&W decals. I simply do not know enough about the #12 machine to be able to tell whether it was built prior to, or after the Singer buyout. I can tell whether a machine is a W&W D-9 or a Singer 9W1, but cannot tell on the #12.
Most likely if you do not find any parts carrying part numbers on them it was made by W&W.? If, on the other hand, you find several parts with a number on them it was made by Singer.
Under Singer nomenclature, there were three basic versions of the #12. 12W1 to 12W99 were Short Arm machines. 12W100 to 12W199 machines were Long Arm machines.? 12W200 to 12W299 were High Arm machines, which were also short. When you see the term Drop Feed in this catalog it is referring to the regular 4-motion feed in contrast to a wheel feed, which was quite popular on leatherworking machines. I do not know if all of the #12 machines which used the drop feed could also be lowered or not. I found no mention of this in the catalog. Some, though not all of the #12 machines had reverse feed on them. All of these I found were on the drop feed models I did not find this on the wheel feed models.?