Hahaha, hahaha, no. That is absolutely NOT the default arrangement. Unless otherwise negotiated in the contract, the artist retains the copyright for the produced work and is free to use it as they please, including putting it in their portfolio, making further edits to the work, reusing it for other purposes, etc. The commissioner gets a copy of the finished product, but by default has few rights to use it themselves. Technically, I’ve personally infringed an artist’s copyright by cropping a work I commissioned from them to use as an icon. However, the vast majority of artists don’t typw enforce this aspect of their IP rights, due to a lack of resources and also because it would shred their reputation and kill their business.

Explicit transfer/licensure of copyright can be negotiated, but the most artists charge an extremely hefty fee for transferring the full copyright, often double or triple the price of the work itself. Most individual commissioners don’t bother as a result, but commercial organizations looking to reuse the commissioned work must negotiate a license for the work in order to avoid a nasty infringement lawsuit.