Need Jussi to weigh in here as he knows these well. As he helped me understand, there wasn't a slip-on version offered by Termi. These essentially came in a 54 mm asymmetrical system and a 57 mm full system. The 54 mm system replaced the pipe to the horizontal cylinder with a larger 54 mm pipe (no cat) while keeping the smaller stock pipe to the vertical cylinder. I've seen where people have called the 54 mm system a slip-on (or a half system), but the 54 mm option does indeed replace the pipe to the horizontal cylinder. The 57 mm system replaced both pipes with larger 57 mm pipes. These systems came in various versions for grey swingarm vs. black swingarm, deep sump vs. not, stainless can vs. titanium can, etc. For the 57 mm system there were two different styles of pipes, one that had a round section near the right rearset and another that had a flattened section (nicknamed a "banana" system)...the latter to help with clearance between the swingarm and the fairing.
The asymmetrical system is what is generally called the slip-on, it does come with a replacement pipe for the front cylinder since the OEM pipe houses a cat.
The asymmetrical Termignoni can has two pipes of different diameter and length sticking out of it.
The mm of asymmetric system is irrelevant since there are no variations in diameter available. The vertical pipe differs from horizontal one in diameter and length.
The asymmetric system comes in variation Deep / shallow sump, and grey/black swingarm
The symmetrical system comes in 2 different pipe diameters, 54 and 57mm, generally speaking the 54 was more intended for 749, however I have read of people using it on 999 without loss of power.
Canisters for both are dimension wise identical but available in SS or Ti.
The canisters have two identical holes in them (no pipes sticking out of them.)
Here the variations are again Deep/shallow sump , black/grey swingarm.
The banana stye pipe is only for deep sump / black swingarm
round pipes can be deep sump / black swing arm ( R versions ) or Deep sump/grey swing arm ( R and S versions )
or Shallow sump,grey swingarm (base version)
So basically when buying full / symmetrical system it is of utmost importance to know what kind of swing arm and sump it was made for.
Otherwise it just won't fit.
When buying a asymmetrical system, it is of lesser importance since you could have your cat removed out of the OEM pipe.
Both came with the DP filters and a DP ECU.
Running the systems without the DP ECU or custom mapping results in too lean mixture and potential engine damage.