I do know the answer to OP's question but that's because I pickle my brain in this stuff. It is legitimately confusing.
The analogy to different SKUs strikes me also inaccurate. This isn't the difference between shoes, shirts, and shorts - it's more as if a company sells three t-shirts but you can't really tell what's different about them.
It's Claude, Claude, and Claude. Which ones code for you? Well, actually, all of them (Code, web/desktop Claude, and the API can all do this)
Which ones do you ask about daily sundry queries? Well, two of them (web/desktop Claude, but also the API, but not Code). Well, except if your sundry query is about a programming topic, in which case Code can also do that!
Ok, if I do want to use this to write code, which one should I use? Honestly, any of them, and the company does a poor job of explaining why you would use each option.
"Which of these very similar-seeming t-shirts should I get?" "You knob. How are posts like this even being posted." is just an extremely poor way to approach other people, IMO.