The Distressor gets its name from its feature of incorporating harmonic DISTortion with a classic knee compRESSOR. For instance, the Distortion 2 setting introduces a 2nd order harmonic, which adds tube-like analog warmth to the signal and the Distortion 3 setting introduces a 3rd order harmonic, which simulates tape saturation (great for guitars, bass and drums)!
The original concept of the "British Mode" came from an unusual setting on the classic UREI LN1176 limiter. The unit was designed to have only four ratios, each ratio being engaged by selecting one of four buttons. However, as early as 1980 (or before), renegade recording engineers, always on the lookout for something a little more "over the top", found that you could make all four buttons stay "in" if you pressed them just right. What resulted was a very, very aggressive sound that had some elements of the units 20:1 ratio, but with an unusual knee and new envelope shape. Somewhere along the line, someone called it a "British Mode" and the name has stuck. It is also called "all buttons in" and some other intuitive names.
The Distressor has the advantage of being able to apply this "aggressive" nature not only to the new British ratio (1:1) but also to all the ratios since a separate switch is installed, which can be enabled with any ratio. One should keep in mind however, that an attack below 3 or 4 is required to maintain the LN1176 character. If you go above an attack of 3 you will also incur a rise in some grunge (distortion) and see the THD indicator lites come on a lot more.