In my opinion they are basically the same, however there are different degrees of this.
Its all in termology and understanding of the concept. The word channel is more a new age term which I beleive started being used around the 1970's onwards, before that people were called Mediums and even further back called oracles.
Some old school people may still debate different termology however in my eyes they are describing similar concept.
In most forms of energy healing you are being a channel, this is likened to being a hallow bone for healing energies to flow from source through you to the recipient you are working on. A channel is allowing energies to flow through you weather this is healing energies like practiced with spiritual healing or information coming from a higher source as in mental mediumship.
There are two aspects of Mediumship, Mental and Physical.
In mental mediumship all the information is recieved through the mind of the medium and then passed to the sitter. With physical mediumship everyone that is there at that time can see and hear what the other can, you do not need any psychic ability to be able see, hear or even feel is being shown. If there are only some people present that are aware of the phenomenon being produced in the room and not everyone then it is not physical mediumship.
In mental mediumship it is then broken down into two categories, Perception and Control.
With preception the medium enters an altered state of consciousness and while in this altered state the medium/channel connects with spirit to receive information/messages and then passes it on to those present, in my opinion this is also called channeling. The medium is the inbetween and often you will hear the term dont shoot the messenger. This is done on a level of consciousness or semi consciousness where the medium is aware on some level of what is happening
With control, you are usually looking at deep trance. Be aware this is still mental mediumship and often the medium has no recollection or memory of what has taken place. In trance the medium has usually spent years studing and learning about mediumship and under the guidence of a knowledgeable teacher has taken there mediumship up to the next level. I do not recommend a person moving into trance mediumship lightly and without the right teaching and guidence. In control a medium will have build up a trusted relationship with spirit guides and have what is called a spirit operater which they allow to influence them in what they say and do. In deep trance the spirit operator may use the mediums body and have the ability to operate with the mediums permission, the vocal cords and other body parts usually operating through the nervous system knowing what to trigger . The spirit operators at NO time enter the body, there is only room for your own spirit within your body, spirit operators only have the ability to influence the body with the persons permission.
Even with deep trance the mediums consciousness cannot be removed and there will always be a element of human influence in the information passed on. However in my opinion the deeper the trance the more pure the communication from spirit.
I hope this has helped a little with understanding mental mediumship.
Blessings Misty