I would propose that of the three equivalent terms - module, adventure, scenario - we use adventure. Scenario is more technically correct but it's also not what the average Joe searches for. I think adventure is more accessible (as is proven by scenario's use in only one of these tags with 13 occurrences, as opposed to module with 14 and adventure with 73).
We would then have:
- published-adventure synonyms: published-adventures, modules,
- adventure-writing synonyms: scenario-authoring, adventure-design
We could then preen the adventure questions to put them into the right category... Those have some bad overlap with campaign as well, cf. Any good premade campaigns for beginners?. Once all 40 questions are disposed of, synonym adventure to adventure-writing. A pure adventure (or module, or scenario) tag is so vague as to be unhelpful, since it cam be used to describe everything PCs do in play and most of what GMs do in prep for play.
There is also adventure-path which is an interesting case - given that there is a question What is an Adventure Path? I guess there is a niche in there right between published-adventures and campaign but it's narrow - I'd leave this be for right now but keep an eye on it.