It's wildly confusing branding not only because they're identically-named things that both repackage OpenAI's LLMs, but also because they're both ultimately owned by the same company.
I can only assume that the conflicting naming convention was either due to sheer incompetence or because they decided that confusing users was advantageous to them.
Haven't tried it yet but the GitHub Copilot extension for VSCode also seems to integrate Claude, Gemini and other non-OAI stuff
The Claude Code extension for VSCode from Anthropic will use your Claude subscription. But honestly it’s not very good - I use it but only to “open in terminal” (this adds some small quality of life features like awareness it’s in VSC so it opens files in the editor pane next to it).
Larger than the difference between the .Net Framework (that is a framework) and .Net Core (that is a framework)?
The only good "AI" editor that supports Claude Code natively has so far been Zed. It's not PERFECT, but it has been the best experience short of just running Claude Code directly in the CLI.