Understanding AJAX Database Calls

I'm trying to teach myself Javascript. I've used jQuery and understand it, but I'm trying to learn how things actually work under the hood. I've been teaching myself some AJAX techniques and I'm wondering, purely out of curiosity/theory (in spite of the obvious security risk) if it is possible to make a database connection from the client-side in pure Javascript?

I understand GET/POST requests and I kind of understand XHR and JSON protocols, but I'm just wondering if that's the same or different than a direct database connection from the client-side with JS, without any server-side scripting like PHP. Or, are async calls always constrained to GET/POST and/or server-side scripting? If not, are there other methods?