What is the difference between
Do some mean that the BGA is soldered to the board and cannot be removed? BGA is soldered versions only, right?
What does "FC", "PG" and "988", "1224" mean, etc.?
The numbers are the number of pins, and kind of tells you which motherboards it will go into - the current Ivy Bridge Desktop Boards use LGA 1155 sockets - LGA means Land Grid Array - the pins are on the motherboard, not the chip.
BGA means Ball Grid Array and yes, it does mean they are soldered on through little balls on the underside of the package. If you had specialist equipment you could in theory desolder that and resolder a new one. I doubt too many people have access to a reflow oven tho
PGA means Pin Grid Array, which means the pins are on the processor, FCPGA simply means the chip is mounted upside down, and rPGA simply means the 'pitch' or distance between pins is less.
Together, these should give you a rough indication of what chip would physically fit into a socket - no chance of me putting an old c2d era LGA 775 (with 775 pins) into a modern LGA 1155. You will also need to check if the bios will work with the chip you want.
Get a chip of the same packaging type - for example, if your current chip is a FCPGA 998, get a chip that's also FCPGA 998, and a good bet might be to get a chip thats used in a different SKU of your laptop.
Upgrading laptops is a bit of a crapshoot though, and its likely to be tricky.