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These APIs are only for use by host controller drivers, most of which implement standard register interfaces such as EHCI, OHCI, or UHCI. UHCI was one of the first interfaces, designed by Intel and also used by VIA; it doesn't do much in hardware. OHCI was designed later, to have the hardware do more work (bigger transfers, tracking protocol state, and so on). EHCI was designed with USB 2.0; its design has features that resemble OHCI (hardware does much more work) as well as UHCI (some parts of ISO support, TD list processing).
There are host controllers other than the "big three", although most PCI based controllers (and a few non-PCI based ones) use one of those interfaces. Not all host controllers use DMA; some use PIO, and there is also a simulator.
The same basic APIs are available to drivers for all those controllers. For historical reasons they are in two layers: struct usb_bus is a rather thin layer that became available in the 2.2 kernels, while struct usb_hcd is a more featureful layer (available in later 2.4 kernels and in 2.5) that lets HCDs share common code, to shrink driver size and significantly reduce hcd-specific behaviors.