That's a complex question. The Apple Newton was the first "PDA" (Personal/Portable Digital Assistant) - the first hand held PC's. Then came the Palm Pilot - both basically did the same thing: electronically stored personal address books and calendars. Developers created software for the devices so one could play simple games on the devices. People loved them so the developers kept developing and technology kept growing and changing. Then came the cell phones with more developers getting even more creative.
Research in Motion (RIM) created the Blackberry - the first portable device to make e-mail available anytime, anywhere. People loved the Blackberry, Palm felt threatened and created the Treo - basically a Palm Pilot that was also a cell phone.
The came the iPOD - the first portable MP3 player - all they do is play music that you download from the Internet; wireless devices are coming this Xmas.
Blackberry, Palm, Treo, and phone companies felt threatened, but saw that they could combine the technology into one device. So, today you have phones that are PDA's, PDA's that are phones and also play MP3's and surf the internet. etc. The sidekick is a PDA/phone and I think it also plays MP3's.
What the devices does depends on the hardware & software. I carry a Palm (Palm dropped the "Pilot" off their name years ago). It has my personal address book, calendar, games, ebooks, photos, plays MP3'S. With a WiFi attachment I could event get e-mail on my Palm, although I'm a purist and like my Palm to just have my life in it. I'll use a real PC to surf the 'net and don't want to have to pay yet another wireless provider for e-mail on my Palm.
Not sure if this answers all your questions, but I tried.
Edit: For a really techie intensive article on the history of the PDA: http://www.snarc.net/pda/pda-treatise.htm
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