Mixer controllers, such as the Hercules RMX, are designed to mimic the layout of a hardware mixing setup. A pair of jog wheels stand in for turntables, and a number of MIDI knobs can be assigned to equalization or effect functions. The benefit of these controllers is the accessibility for those familiar with DJ equipment. They're also not tied to any particular application or platform.
Application controllers, such as the Akai APC40, are specifically designed to be used with a particular piece of software. In the case of the APC, the application is Ableton Live, a popular mixing and recording package. The layout of the controls mimics the user interface of the software, intending to provide a fast, user-friendly alternative to the mouse and keyboard. Such controllers are ideal for DJs who exclusively use a single application, but they can be awkward to assign to any other piece of software. Licensing costs also mean that these units tend to be far more expensive than their generic counterparts.
Most digital musicians have access to a general MIDI controller of some kind --- a keyboard, drum pad or box of assignable rotary controls. Any application that accepts MIDI input can be programmed using its "MIDI Learn" function. Buttons and keys on a drum pad can be set to trigger samples and start playback devices, and rotary knobs can be assigned to crossfaders and pitch controls. This method is cheap and accessible, but it's important to memorize properly which buttons and dials have been assigned to which software controls. Since drum pads and keyboards weren't designed with DJs in mind, the custom layouts are generally not intuitive.
Since around 2005, a number of so-called "abstract controllers" have started to appear on the market. These devices generally do away with any sort of familiar recognizable control surface and are geared more toward evolving, improvisational structuring. Units such as Yamaha's Tenori-On, the JazzMutant Lemur, Korg's Kaoss Pad and Roland's D-Beam can all be assigned to handle DJ functions, all without any traditional "knobs and faders." As is implied by their design, they are intended for experimentation and exploration, and they might not be suitable for someone simply wishing to mix a few records. For those wishing to go a little further afield, they offer a new approach to control surfaces that could yield interesting results not possible with a traditional controller.