this is from memory so may be a little incorrect.
Retail boxed CPU's are covered under retail terms and conditions, so if the retailer offers a 12 month warranty and your CPU fails outside this period, for example AMD would pick up the remainder of the warranty up until 3 years.
OEM processors are usually supplied to system builders, Dell spring to mind, as then Dell will offer warranty on their systems as part of the selling tool. If you buy OEM processors it is up to the supplier to state a warranty period, 1 day if they so choose and AMD (again for example) are not bound by any conditions to pick up the remainder of any warranty.
There are quite a few I know of in the UK that do this, I'm not going to name names but they do it on a lot of products not just CPU's.
Grey Importing again this is sketchy and from memory from my distribution days - can be stock that is brought in to the UK that was not Uk allocated stock, this can cause problems with warranty (as manufacturers serial track CPU's so can tell for which market they were intended) and again refuse warranty etc.. these grey imported products are usually sourced via the VAT carousel through Europe or from the Far East where even fake or reboxed CPU's can be bought, hence the introduction of holograms on CPU boxes.
Basically all CPU's can be serial traced, if you buy OEM and try to pass it off as Retail, you'll get found out, if you buy in grey and try to claim warranty, you'll get found out.
Best bet is to always buy a retail boxed CPU from a trusted seller, if it seems too cheap then it's more than likely a grey import or vat carousel stock and you may come unstuck with warranty. A lot of companys, us included, serial trace all cpu's we send out, so if someone for example, buys OEM, blows it up then buys a retail boxed one from us, sticks the blown OEM back in the Retail box and tries to return it as faulty for a refund hoping to get away scott free with a new processor, we can trace what serial number went on that order and if the numbers don't match, then they're out of luck and will not get the refund, trust me people try.........
I did this with a Digital Camera I bought from a certain on line retailer, when I registered it with Fuji as the warranty states you have to do so, they informed me my camera was under no UK warranty regulations as it was actually intended for the American market even though it is exactly the same as the camera on offer in the UK, basically the supplier had bought in cheaper cameras of the same spec and model from the USA to avoid paying the higher European price and I got stiffed with a camera with no warranty that they refuse to take back