Almost. It's the current prompt plus the previous prompts and responses in the current conversation.
The idea behind "context engineering" is to help people understand that a prompt these days can be long, and can incorporate a whole bunch of useful things (examples, extra documentation, transcript summaries etc) to help get the desired response.
"Prompt engineering" was meant to mean this too, but the AI influencer crowd redefined it to mean "typing prompts into a chatbot".
Haha there's a pigheaded part of me that insists all of that is the "prompt," but I just read your bit about "inferred definitions," and acceptance is probably a healthier attitude.