Earlier quoted context omitted.
While every OS ships with a browser, I think the OP was asking "do you have to install windows 10" in order to get the new MSFT Browser. IIRC, those examples you listed, you don't need to install the latest OS X to get the latest version of Safari (though you need to have a recently supported OS).
You can't use Safari 8 on Mavericks. In a sense they backported some features to Safari 7 (as well as security updates, etc), but it's a distinct version and a very different browser.
Many versions of Safari are coupled with OS X updates.