These are general terms and often overlap. Mediumship is the practice of communicating with the spirits of deceased human beings or animals. A medium is usually conscious and typically relays short personal messages from a loved one or animal who has passed. The main purpose is to provide comfort through evidence of survival. 

Channelling is the practice of serving as a conduit for more universal messages from non-physical consciousness. The source may be evolved humans or guides, higher beings, ascended masters, collective intelligences, universal or cosmic consciousness, interstellar beings or higher self. Usually the messages are more extensive and philosphic and the channel enters an altered state.

For examples see Kevin Moore's YouTube series
"They Call us Channelers".