Generally, don't removed soldered chips unless you understand what you're doing and have a reason to do so.
Most of the socketed computer CPUs are fairly straightforward.
Separate into ceramic and fiber. Ceramic is cooler to the touch and are usually more pink/purple or white in color, while fiber is made of the same material as circuit boards and typically are green, brown or black.
Separate with and without a heatspreader or gold cap.
Separate with and without pins.
On fiber, without pins basically all look the same. May have variations in the size or specific arrangement of the LGA (land grid array)
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Still on fiber, with pins with metal these are basically a male end going into a female socket. It doesn't really matter how big the heat spreader is, if there is one it is "with metal" If you end up with this type CPU that has been damaged and lost a lot of pins keep it separate or ask ahead of sending it in how to sort it.
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Fiber, with pins but no metal, is exactly the same as the previous but without a heatspreader. I have removed the metal in the past as a means of fitting more chips into a USPS Large Flat Rate shipment; it WAS NOT Worth it. Unless you have a local yard that pays really well on the copper there is no reason to bother doing that.
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The last main group of fiber is Slot Processors which have a very distinctive Single Edge Contact Cartridge (SECC and other abbreviations for different versions, just google CPU socket if you're curious). Boardsort's example is the bare board but they often have a case.
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That's all I got right now; not feeling great. Hope it helps.