hi,
Yes, a Pixaxe is a programmed PIC that you have to use Picaxe Basic to write its programs, which are then loaded into the PIC by the user.
A PIC is an unprogrammed IC, which the user has to write programs in C-compiler or Assembler, the hex files are then programmed into the PIC by the user.
EDIT: when you buy the Picaxe IC , it has already been programmed with their Picaxe interpreter
I think the small bit is an understatement, the picaxe interpreter takes a BIG chunk out of the pic and leaves a bit for the user. Also the speed is throttled right back and when a user wants to upgrade to the real world one will have to start from scratch.....
Also a BOOTLOADER is known as a boot strap from what I have learnt and yes it is only a small program