Deepseek refers to a lot of different things and I think that's where some of the confusion is coming from. There's the huge model, the company, the smaller models that they trained about a year back, and the service that company runs with an online frontend connected to their large model running on their servers. The latter absolutely can harvest data you put into it. And I'd assume they do. All the large companies running them do unless they say otherwise in their TOS. And even if they say they don't, I'm a little skeptical.

But the short of it is that a fully local model can't communicate with outside parties unless it's been specifically linked with tools to let it do so on your computer. Even when they are provided with those tools you're often stuck reminding them to actually use them. And most GUI frontends will put up some form of notification to alert you to the fact that those tools have been triggered.

I skimmed over the deepseek unchained thing and I'd say it's pointless. I couldn't find any concrete explanation of what it actually is either. My guess is that they're talking about the smaller qwen models that deepseek did additional training on. They were talked about a lot by the popular press as "local deepseek" for a while. But they're really more like a quick experiment deepseek did with so-so results. They're essentially obsolete these days as better local thinking models have overtaken them. What people generally mean when talking about the deepseek model is a huge one that almost nobody could run locally anyway. However, some american companies do host that model if you're worried about anything related to china. Chinese model but american servers mean that the companies need to comply with US law.