From what I'm reading online, iaido is a collection of arts related to swords (not just drawing them off a scabbard, but also things like cleaning and sheathing them) while battoujutsu is specifically the art of being ready to draw the sword. Most posts under that tag are ready-to-draw stances, but there's a few odd cases:
post #3629181: generic sword kata. We don't have a tag for generic sword exercises as far as I know (correct me if I'm wrong), and I think a more generic tag would be better than "iaidou" for this
some random posts where katana are not being drawn (post #3856384), which I assume were tagged because of translated tags.
I'd rather just empty the iaidou tag and remove the translated tags, because an alias would risk having people blindly pulling the tags, a risk accentuated by the fact that nobody's going to know what "battoujutsu" is without reading the wiki and nobody's going to read the wiki (this has already happened with iaidou as seen in the example above).