Pretty much what Mark said with the following clarifications:
Smartphone has been used in more than one meaning for years. The general meaning is as Mark describes - any phone that also has PIM and/or PDA functionality (calendar, tasks, contacts, etc.)
However, both
Palm and Microsoft have used the term to specifically refer to either their phone (
Palm and the Treo series) or their operating system powering the phone (Microsoft and the "Smartphone" OS that is found on the Motorola Q and Samsung Blackjack, for example.) To further muddy the waters, Microsoft calls their "smartphone" version Windows Mobile Smartphone, which is a derivative of the Windows Mobile OS used on touch-screen devices like the
HTC Touch, the xv6800/PPC6800 and the AT&T Tilt. Microsoft's smartphones do not have a touch screen - instead they use a cursor with either a jog wheel or 5-way button to move the cursor around the screen.
A typical PDA would be one of the old
Palm Pilot handhelds or an HP iPaq. No cell phone built in... which makes a
PDAPhone a hybrid of both cell phone and PDA.