I think some vets also use the terms a little interchangeably - so they might refer to a very light, quick GA as 'sedation' to make it sound less scary. I see it as a spectrum rather than two separate things, where sedation could be very light or very heavy, and when the animal is fully anaesthetised I would say it was under GA. I wouldn't say that sedation is necessarily just gas, it could it not just be smaller amounts of the induction agents without the gaseous maintenance?
For me, the issue with a minor dental every 4-5 weeks is more that a good thorough dental under GA might only be needed every 4-5 months or even less if the teeth can get themselves back into normal occlusion from some good detailed dentals. Just doing a quick skim under light sedation might take off sharp points but it won't allow a full burr and re-shape to just above the gum, so it's pretty inevitable that it will need doing more often.