No, this doesn't seem to be correct, although confusion regarding model names is understandable.
o4-mini-high is the label on chatgpt.com for what in the API is called o4-mini with reasoning={"effort": "high"}. Whereas o4-mini on chatgpt.com is the same thing as reasoning={"effort": "medium"} in the API.
o3 can also be run via the API with reasoning={"effort": "high"}.
o3-pro is different than o3 with high reasoning. It has a separate endpoint, and it runs for much longer.
o4-mini-high is the label on chatgpt.com for what in the API is called o4-mini with reasoning={"effort": "high"}. Whereas o4-mini on chatgpt.com is the same thing as reasoning={"effort": "medium"} in the API.
o3 can also be run via the API with reasoning={"effort": "high"}.
o3-pro is different than o3 with high reasoning. It has a separate endpoint, and it runs for much longer.
See https://platform.openai.com/docs/guides/reasoning?api-mode=r...