I like the term "asynchronous coding agent", which I define as the category of coding agent which runs in a container somewhere and files a PR when it's done.

OpenAI Codex Cloud, Claude Code for the web, Gemini Jules and I think Devin (which I've not tried) are four examples.

I like that "asynchronous coding agent" is more specific than "asynchronous agent" - I don't have a firm idea of what an "asynchronous agent" is.

One catch though is that the asynchronous coding agents are getting less asynchronous. Claude Code for the web lets you prompt it while it's running which makes it feel much more like regular Claude Code.