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They are all microcontrollers. PIC is just "Microchips Corporation" designation of the chips that they manufacture. I think it it means something like programmable industrial controller, someone may correct me on this. Whatever the manufacturer they all do much the same sort of thing, just different op codes, functions etc. Pics are a good way to start learning though.
I think it's all about the availability in the market. You can find anywhere a PIC controller whatever electronic shop or store you pop in. It is cheap, so just you throw it away if broken. I agree with GrandAlf, they are good to take a start for learning how to use microcontrollers.
AVR is produced by Atmel. You get different models of a company's uController.
It is possible for example to get a PIC and an AVR that has the same functions.
With functions, I mean for example the same amount of memory, communication methods etc.
I have used PIC, Renesas and AVR. My favourite is the AVR, because of all the online support. Check out www.avrfreaks.net.
But as they said, PIC's are easy to get and have been available for a long time.