So, the Assistant API in OpenAI is just a wrapper over the Chat API. They let you choose which model you would like to use, so as a result of you fine tune a model you should be able to use it.
However I never tried fine tuning, I rely on RAG and the Assistant API does provide you some tools to make this a bit easier. What tools? They provide an "editor interface" where you can set function calls, upload some files and access the code interpreter.
So if you are making a chatbot for Company Y, you can create an assistant which has information about Company Y in the system prompt and also can access up to date information about the company through function calls you define and the files you upload.
If you use only Chat API, you will have to handle these stuff yourself. Actually, though I'm using Chat API I do use the Assistant Editor UI to manage the functions and the system prompts. What I do is, I retrieve the assistant info from the OpenAI Assistant API and then I use this on Chat API. This way I don't have to bother with creating my own UI or fiddle with text files or the code.
As Assistant API is just a wrapper, most the data structures I receive from Assistant API directly work in Chat API.
