I think there are a lot of people who use "Wet Shaving" interchangeably with "Traditional Shaving," and it can be confusing.
In my opinion, here is the difference:
Wet Shaving: Not dry shaving
Traditional Shaving: Using a soap/cream, a brush and a DE/SE/Str8 (which others have pointed out, is also wet shaving with water, I hope!)
What is traditional anyway ? I mean the goo is around for nearly 65 years and take a look at this electric razor from 1932.