The difference is:
ChatGPT has instructions of how to rewrite prompts that appear early in the conversation history. Then you continue having long conversations that alter how substantive those system message instructions are. GPT-4 is always used, as only when it is selected in ChatGPT can you generate images.
The API has its own AI that only rewrites prompts. The idea is presented as “we know what will make better images”, but there’s also lots of “we’ll change undesired stuff”. The instructions should be comparable, but are even more hidden. We don’t know what AI model OpenAI thought was up to the rewriting task in this case.
The last image almost seems like the AI failed. Invoked the DALL-E 3 function, but then produced some garbage that produced some garbage. DALL-E 3 usually makes something much more creative from even just random text, though.
I just generated minutes ago and DALL-E 3 rewrote and produced a cartoony image out of mostly irrelevant language. So API is working.