Mythril Bar

The anvil you build from it unlocks most of the hardmode recipe list. Until you have one, the first metal tier is your ceiling and nothing above it can be made at all. That makes the second mining run after breaking altars the real turning point of early hardmode, not the first.

Your world rolled one of the two and ore will only ever give you that one. They occupy the same slot in the progression and their anvils are interchangeable, so a mythril world is not a worse world. The armor set bonuses differ, and that is the only decision the roll makes for you.

Mithril is Tolkien's invention and the name is trademarked by his estate. An early teaser used the original spelling before the y went in, almost certainly for legal reasons.