I don't understand what do 'for commissions / to commission' mean in contexts from 2 different sorces.
I am an oil painter who works particularly with portraits and other subject matter. I am available for commissions and my other work is for sale on here.
I think I want to commission a few illustrations for our work one of which is a variation on the yin yang.
Commissions are commonly accepted as the term for "requests", when asking an artist (or other content creator) to create a piece of art specifically for you, usually based on your specifications, ideas or designs.
Since being an artist or content creator is commonly regarded as a profession, rather than a hobby, there is an expectation of commercial cost to a commission.
If the artist "does commissions", they are saying that they will accept requests for art, and will create that art in exchange for money. If the artist is "available for commissions", they are saying that they currently have the time (or, more likely, are actively looking) to take on these requests for art and expect to be paid at an agreed rate.
A patron who requests a piece of art or content, to a given specification, can be said to have "commissioned" it, so "I want to commission a few illustrations" is effectively, "I want to ask an artist to make special images for my needs and will pay them to do so."
Note that this is different from someone who purchases a piece of art that already existed, because they like the particular piece (or see potential future value in it), which is why the artist's statement also states that their "other work is for sale". The pieces for sale are likely ones that the artist has chosen to design and create themselves, or previous attempts at commissions that a patron did not choose to buy; while a commissioned piece is one that the patron has designed or described for the artist to create.
An artistic commission (noun) is an agreement, consisting of an offer made to an artist, and accepted by them, to pay for a specified piece of work to be done. The verb means to make such an offer and have it accepted by the other party. It is a form of contract.
There are legal aspects. For example, UK law does not require agreements between consenting adults to be made by any particular method or form in order to be valid and binding. So long as the parties to a deal express their intention to be bound to perform the mutual promises they have exchanged, the law will normally back the deal and, if necessary, the courts will order any defaulting party to fulfil their promises or pay compensation in default. Even if it’s merely verbal, with no witnesses present, it’s good enough. ‘I’ll give you £50 to paint my portrait’; ‘O.K.’ – those words will do.
The verb "commission" is not restricted to the context of requesting artists to produce some work of art. In public administration in the UK is is widely used in the context of one public body requesting/requiring somebody - a contractor, or another public body - to do something.
The whole principle on which the National Health Service in England is organised is that there are commissioners of health services who look to other organisations to provide those services. The idea is that in that way one can restrict the extent to which the providers of services dictate which services are provided and at what cost - the so-called producer-bias.
At one time I held a post in which I was legally permitted to carry out investigations into anything I thought fit. As might be imagined such investigations did not always go down well with the politicians whose work was being investigated. The question they sometimes asked was "Who commissions [me]?". The answer was:"he does".
To add on to the other answers: Be aware in the first example, "commission" is a noun. It's common to say someone "takes a commission" to do some art project.
In the second example, "commission" is a verb. An artist who "takes commissions" can be "commissioned" by someone else (to do an art project).
For the exact definition, we can check the dictionary:
commission
(n): a formal request to do a special piece of work for payment: She received a commission to paint the governor’s portrait.
(v): to choose someone to do a piece of work, or to have a piece of work done: The newspaper commissioned a series of articles on the fashion industry.
