There are currently 78 open questions tagged with deck-building. Of those, approximately 70 are questions about the processes, strategies, card choices, rules, etc. involved in building a deck. This basically corresponds to your first point. The rest use the tag to either refer to deck building games as a category, or in place of a specific game tag in that category.
So, I propose that the best solution here is to keep the deck-building tag for questions about building decks in any game (and modify the tag wiki accordingly), and to retag the other questions as appropriate, either by simply removing the tag, replacing it with a specific game tag, or replacing it with a different type of tag (such as identify-this-game if relevant).