Simply, historical models of artist/consumer or artist/benefactor or patron relationship are:
1) artist working for and/or selling to a larger organization (government, museum, church, etc)
2) artist selling to individual/group consumers, with "collecting" consumers
3) artist selling to individual/group consumers, non-"collecting"
4) artist producing work for ritual, religion*, socio-culture practice** where the consumer's role is perhaps not qualified by exchange of money.
What we commonly call a "commission" could fall under any of these, though I feel that commission is often a relationship that has a high probability of exploiting the artist. This is not to say a commission is good or bad, but practically is up to each individual artist to determine and agree to the arrangement of a commission and often ends with an artist sacrificing many aspects of her or his work to make the commission.
Not included, because it is a different list/relationship:
artist producing work without selling (no consumer)
Consumer purchasing a mass produced piece without an artist (no artist***)
Organization purchasing from a corporation****
*I intend religion here to have more social implications as opposed to "church", in 1), which implies a governing body that commissions a work. Religion, here, is meant to stand for relics, paintings, statues, etc made for religious purposes but are not paid for by the church to further the church's or patron's agenda. The most obvious example of this would be patronage in Italian Renaissance painting.
**I do not mean social practice as a buzzword as it is used too often in contemporary art, but rather attempting to define producing work that has a broader purpose (from the artist's perspective) within society and culture.
***Contrary to any political statements or any other theories, corporations are not artists. Some artists should be considered corporations as they employ many workers and function, organizationally, very much like a corporation in terms of production and their relationship to the consumer (Koons), and I am against this form of artistic production
****These theories are not based on Sotheby's selling to the Met, for example, as both the artists--who will only receive negligible profits from a sale like this in the best case--and consumer are confused, complicated, and frankly have little influence on individual artists.