This isn’t the same thing.

Bluesky has something called fedibridge (third party), where your entire account is forwarded to mastodon and acts like a native mastodon account when viewed from mastodon.

A relay is something that hosts the viewable content on the ATprotocol. Currently, the only relay that encompasses the entire AT protocol is hosted by bluesky PBC, though there are a few very small relays for specific niches.