My friend has a Terraria server running and Rust open at the same time, how can I join their Terraria server?

Solution 1:

You can't do anything to make Terraria joinable when your friend is playing Rust. Steam allows you to join game sessions relatively easily when your friends are playing the same game (ie. you're both playing Terraria, or both playing Rust). However, if you are playing Terraria, and your friend is playing Rust, then you cannot join what does not exist in Steam's eyes.

Your friend would need to set up a dedicated Terraria server that runs your shared world, which you would connect to in-game via an IP address, rather than Steam's "Join Game" feature.