The basic layout of the mixer is described in terms of the number of main inputs and outputs, such as 8X4. A mixer is really a traffic manager. A signal is connected to an input, and you steer it to one of several possible outputs. For instance, you might have five mics on a drum set, and group these so one fader controls all drums. Trombone, tuba and trumpet might go to a group for horns, etc.
Groups usually have the same assignment flexibility as individual inputs.
You might send piccolo, clarinet and bass to the right channel, clarinet and xylophone to the left channel, and the clarinet and tuba to a reverb unit. The output of the reverb may then be brought back and sent to the left and right channels in equal amounts. The quality of the preamps separates the tools from the toys in the mixer world. A pad is a simple push button that cuts the microphone signal by a fixed amount, usually 20 db. An attenuator is another name for the same thing, and sometimes offers a choice of attenuation.