There were phone handsets with buttons on before cordless phones, so as far as the UI goes, there was little major invention initially.

The main inventive requirement in touchscreen phones is in making small, thin, cheap touchscreen modules. The UI concepts that then run on those kinds of devices have however been the subject of design studies for decades before that, and have been implemented in various forms on commercial touchscreen installations.

Also, much of the graphic polish of many of these devices seem to draw a direct lineage to stuff like the old praystation series of websites by Joshua Davis and his experiments with tsunami menus and inertial scrolling elements.