All of these communications channels share the property that they transfer information. The information is carried through the channel by a signal.
A channel can be modelled physically by trying to calculate the physical processes which modify the transmitted signal. For example in wireless communications the channel can be modelled by calculating the reflection off every object in the environment. A sequence of random numbers might also be added in to simulate external interference and/or electronic noise in the receiver.
Statistically a communication channel is usually modelled as a triple consisting of an input alphabet, an output alphabet, and for each pair (i, o) of input and output elements a transition probability p(i, o). Semantically, the transition probability is the probability that the symbol o is received given that i was transmitted over the channel.
Statistical and physical modelling can be combined. For example in wireless communications the channel is often modelled by a random attenuation (known as fading) of the transmitted signal, followed by additive noise. The attenuation term is a simplification of the underlying physical processes and captures the change in signal power over the course of the transmission. The noise in the model captures external interference and/or electronic noise in the receiver. If the attenuation term is complex it also describes the relative time a signal takes to get through the channel. The statistics of the random attenuation are decided by previous measurements or physical simulations.
Channel models may be continuous channel models in that there is no limit to how precisely their values may be defined.
Communication channels are also studied in a discrete-alphabet setting. This corresponds to abstracting a real world communication system in which the analog->digital and digital->analog blocks are out of the control of the designer. The mathematical model consists of a transition probability that specifies an output distribution for each possible sequence of channel inputs. In information theory, it is common to start with memoryless channels in which the output probability distribution only depends on the current channel input.