Definitely PDA. Before we had modern smartphones folks would carry a cell phone and separate PDA which had computer functionalities. I've always said they were smartphones with half the smart and none of the phone.

Common apps included calculators, calendars, to do lists, notepads, clocks with alarms, task lists with reminders, PDF readers, word processors, later ones could even double as mp3 players and portable video players. There were even games made for them, both official and homebrew. My Windows PDAs have a bootleg port of XCOM: UFO Defense on them, which works brilliantly! There's also ports of Space Trader, if you want to take Elite with ya in your pocket.

PDAs evolved into smartphones as companies started including cellular tech inside PalmOS and Windows Mobile PDAs with devices like the Palm Treo and HTC Apache running PDA OSes with cellular connectivity. Once the iPhone came out though basically everything changed. They weren't the first, but they released a slick, buttery smooth device using a much better type of touch screen, with heaps of built in flash memory, a vibrant high res screen, and of course, iTunes. I own a PDA from the same year, not lower end but kinda middle of the road. 128 mb of usable flash memory, 64 mbs of RAM, a 240x320 resolution 16 bit color resistive touch screen (pressure sensitive, like the DS), a full sized SD card slot which can take up to 2 gigs of additional storage, wifi, Bluetooth, and IRDa. Required a stylus for usage. Versus the iPhone, which had anywhere from 4 gigs to 16 gigs of built in storage, 128 mb of RAM, a 480x320 resolution 18 bit color capacitive touch screen, Wi-Fi, Bluetooth, and multi-touch functionality on the screen. No stylus needed, either.