No.
Palm is a company that makes both a PDA and a PDA OS and both are called Palm. Other companies have licensed the Palm OS, the two most notable are Handspring and Sony. The new Sony Clie PCG-NR70 is a wonderful device that includes flip open keyboard and MP3 player.
PocketPC is any PDA running the Microsoft PocketPC OS. The PocketPC is much more processor intensive with 200+MHz processors instead of the 33MHz common on PalmOS devices. They are also more multimedia capable than Palm though Palm still has more software available to it. One of the significant differences for me with PocketPC is the networking capability. It has real TCP/IP networking allowing for direct web surfing and best of all, Remote Access to my WinXP box. It's slow and the screen is cramped considering most sites are designed for at least 800x600, but it's workable and you don't need some reformatting service or WAP enabled site.
There are other PDAs on the market like the Franklin organizer, but they are bit players in a limited market.
With color screens both Palm and PocketPC have lower battery life than the old B/W PDAs with average time in the hours instead of days/months level.
No PDA today has good handwriting recognition. At least not compared to the Apple Newton. Both Palm and PocketPC have a special character set you can learn that enables you to write almost normally with block letters. There is add-on software, often included with various PocketPC models, that supposedly allows "natural" handwriting recognition, but in my experience it doesn't work that well.
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