To answer your question, wet shaving is when you make your own lather with soap or cream and water. I don't call shaving in a shower with an electric or using foam from a can "wet shaving" - but that's just me. You are right: you can wet shave and still use a cartridge. That's why I don't use the term wet shaving. I call what I do traditional shaving. To me traditional shaving is wet shaving and using a DE, SE, injector, or straight razor.
You can do multi-passes with a Mach 3. However, every time you make a pass with a four or five bladed razor it's as if you are doing four or five passes. No doubt irritation, ingrown hairs, etc. may well result.
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A couple of questions I haven't had answered yet.