“Appliance” in marketing lingo doesn’t really refer to a type of server, per se, but a type of packaging or bundling. In fact, the term “appliance server” simply refers to any type of server that is sold already set up and configured, and ready to be added into a network. So, when IBM markets its “eServer xSeries 130”, described as a Web-hosting appliance server, it is really selling a Web server — probably a dynamic Web server also known as an application server — bundled as “plug-and-play” as is reasonable for installation into an existing network.
Similarly, IBM’s “eServer xSeries 150” is called a storage appliance, which basically means it is a file server to and from which users can store files.
Presumably, the term “appliance” is supposed to connotate the idea of a server — any type of server — as ready-to-use, just as a kitchen appliance, such as a refrigerator or stove, is basically usable out of the box.