What is is called when you have a delivery with drugs, vag style?

you are right about natural. it is just called a vaginal delivery or a vaginal delivery with pain medications. it doesn’t really have any sort of special name.

Generally, the most common form of pain relief medication that women use to still give birth vaginally is called an epidural, which is a medicine injected into the spine through a needle and numbs the lower half of the body. Most often, women with an epidural cannot feel pain, however they do still feel “pressure” especially during pushing. Hope this helps!