Fine-tuning is distinct afaik... using OpenAI's language for it[1]:

zero-shot: no examples in the prompt, just an input (and/or instruction)

few-shot: one or more examples of input+output in the prompt, plus new input

fine-tuning: updating the model with examples (which can then be used with zero- or few-shot as you wish)

[1] https://help.openai.com/en/articles/6654000-best-practices-for-prompt-engineering-with-openai-api (part 5)