My understanding is that NVidia and ATI both have a single unified proprietary driver each, named nvidia and fglrx respectively. Those drivers are closed proprietary binary blobs over which Linux developers have no control.

There are also open source replacements of those drivers, named nouveau and radeon.

Intel, being in this case more open-source friendly, opened their driver, so there's just one open source driver, named intel,

All of those drivers support all available graphic chipsets from the given manufacturer (maybe except ancient ones). When a new chipset appears, the support is added to the driver; also the support for very old chipsets is sometimes dropped, which means that if you have an older machine sometimes you want to install an older version of the driver. Apart from that, there are no drivers specifically designed for a particular chipset.

On the other hand, if you don't have, say, an Nvidia card in your system you won't see nvidia driver in the Additional Drivers. So yes, Ubuntu only shows drivers which are designed for your hardware, but no, those drivers are not for designed for one particular chipset only.

Open-source drivers are installed in Ubuntu by default. If Ubuntu detects that there are proprietary drivers available for your hardware, it lists them in the Additional Drivers dialog. You're actually not required to install those drivers, if you don't you will continue to use the open source drivers.