Starting from the most basic principles of silencers, the goal is to provide two things: volume for expanding gasses, and a means of dissipating energy (thermal and kinetic). Aside from genuinely novel designs like OSS, this is accomplished with baffles that impede the flow of gas.
Cans have come a long way since the days of steel / copper wool packing, leather wipes, and flat washers.
Now you have a multitude of designs all tailored to perform under specific circumstances. Radial and K-baffles for subsonic rounds, cones for high velocity rounds, omegas for a wide range... the occasional can that incorporates wipes when being super quiet is more important than longevity or accuracy.
Materials are used based on what goal you are trying to achieve as well. All stainless on a .22 can so it can be pin-tumbled or "dipped" to clean. Aluminum for light weight and cost savings. Titanium for light weight and longevity. Inconel and 17-4 stainless to withstand blast pressures of large rounds. A mix of materials to balance cost/weight/longevity... you get the idea.