I guess the W is to differentiate it from Systems Engineer?
We use SE here in Japan for both software engineers and system engineers. How are they difference? The latter is older and seems to have originated from people doing architectural, consulting type of work.
Fun fact, consulting/contracting businesses here and also known as SES, System Engineer (as a) Service.
I have no idea who started using these acronyms but they definitely forgot they're new and not universal.