Why Can an OpenAI API Request Hit a Token Limit Before the Model’s Context Is Full?

I’m trying to understand OpenAI API limits and keep seeing requests fail even when the conversation seems comfortably below the model’s advertised context window. Are per-minute token limits and the context window separate constraints?

It would help to know how input tokens, generated output, and concurrent requests affect the limit. I’m not looking for a particular code fix so much as a clear way to tell which limit an error is referring to when building an application.