Indeed, usually the ownership of the product is defined in the work agreement between the client and the executor. Generally, the client holds the actual ownership rights of the products that were produced during the work for them. However, the original creators or contributors to the production may be referenced in the credits of the product.
As for intellectual property rights, the actual creators retain the intellectual property rights to the work, which include attribution, the right to modify the work, and the right to commercial use of the work. Generally, anyone who wishes to use the work for commercial purposes needs to obtain permission from the owner of the intellectual property rights to the work.