Unlike copyright, ownership of a trademark is not about who created the mark. Trademark rights are created by using the trademark for goods and services in commerce. So when you create a logo for a client, your client will own trademark rights in that logo as soon as she starts using the logo on products or promotions for her company.
A trademark is any phrase or symbol that functions as a brand, that is, it tells the public that there is a particular source or manufacturer for products or services. The scope of what can be a trademark is very broad-words, images, sounds and colors can all function as trademarks. Even packaging and promotional concepts for products or services can be protected as "trade dress," which is another form of trademark rights.