Data format to train assistant based on user-support dialogs

Is fine-tuning of a “gpt model” smth different from creating and finetuning assistant created withing openAI assistants API (which I was originally referencing)?

And what is in my case more appropriate then? My final goal is to connect the assistant to smth like livechat (with my mediator which will take message from user, send the to openai (whatever assistants api or completions over fine tuned model or whatever is more suitable), and return responce back to user.