I have a longer version of this, but in summary

So my understanding of the differences between chat, code and co-work; but may well be wrong!

Chat is the human, talking directly to the LLM - old school. Very basic can create docs etc - but saves in a temp folder. No real access to your local PC.

Cowork / work - Human talking to an agent, which can then use tools to do work. Also runs in a container, allowing it access to your drives/computer.

Claude Code / Codex - No longer in a container, full access to the computer, depending on what permissions you give. No longer locked in a container. + The agent is more focused on coding than cowork / work.