The WPB is not short hand for any process. It is simply an identifier developed by ASTM. The fittings in question are manufactured in the same manner as the companion pipe for this specification.
In very large sizes, the fittings may be manufactured in pieces and welded together as is the case for many large fittings.
The term used for the manufacturing is called “wrought” which means it is worked as opposed to being cast or forged.
As to the W standing for weldable, I’m not sure that is correct since that are many, many pipe fittings that are weldable but carry designations other than a W. Note the reference below.
Forging is the manufacturing process of ASTM A234 WPB pipe fittings.
W = WELDABLE / wrought
P = RELATED TO P NUMBER OF ALLOY MATERIAL
B = REFER TO MINIMUM YIELD OF MATERIAL
Latest standard is:
Standard Specification for Piping Fittings of Wrought Carbon Steel and Alloy Steel for Moderate and High Temperature Service
This standard covers wrought carbon steel fittings of seamless and welded construction which are manufactured to the dimensional specifications of ASME B16.9 and B16.28. These fittings are primarily for use in pressure piping and in pressure vessel fabrication for service at moderate and elevated temperatures.