Hey, run locally in this case means: YakGPT has no backend. Whether you use the react app through https://yakgpt.vercel.app/ or run it on your own machine, I store none of your data. I will try and make this wording clearer!
In that case you're basically offering a browser-based client. 'Locally' strongly suggests this is running entirely on the machine (vs. making API calls). Going to break a lot of hearts out there with the wording as it is.
It is more local than talking to chat GPT directly. Open AI stores all your requests on their server. This saves it on your computer. The title also claims it's a UI which always, for now, runs locally.