Isn't this what they already say agents can do?

Can someone who knows more about AI agents explain this to me?

Axios quotes an Anthropic spokesperson re: the Claude leaks, who says that this new capability is coming: "A "persistent assistant" running in background mode that lets Claude Code keep working even when a user is idle. "

Isn't that what they claim "agents" are doing already? Or am I missing something? I would hate to learn that "agents" are just a marketing term and they don't actually do the thing these companies claim... ;)