The trapox was attached directly to the exhaust manifold, upstream of the turbocharger. It's a vaguely football sized-and-shaped (Uh, US football, that is...) thing right next to the valve cover. If it has been removed you'll instead have a straight pipe in that location, covered with some shiny aluminum insulation.
The trapox was literally a soot filter. It was composed of a ceramic matrix built on steel rods. It literally trapped carbon particles. In theory it got hot enough to eventually burn the trapped carbon, reducing it to CO2. In practice, it didn't always work. Cars which did not see at least occasional aggressive use had the trapox slowly plug. Initially performance was reduced, eventually the engine overheated. Some have blamed the occasional OM603 head failures on this overheating, but I don't think there's 100% correlatation.
Another failure mode of the trapox was for small particles of the ceramic matrix to break loose and sail down the exhaust stream. This was rather unfortunate, as the next thing downstream was the turbocharger. When the ceramic material impacted the turbine blades spinning at 100K RPM, well, let's just say it was ugly and MB gave away more than a few free turbos.
The oxidation catalyst performs much the same function, though I believe it is constructed more like a typical catalytic converter. It doesn't literally trap the soot particles, in other words. It's located downstream of the turbo, where it can't do quite so much harm.