i am writting this, because upsilon had a great tread on this topic, but due to forum changes, lots of threads may have been wiped out..
his thread was detailed, highly informative and had half naked chic pics, (typical him :p) , this is just a summary..
Korean phone is the BEST and most authentic version of a phone from LG and Samsung. Korea is the birthplace and Original factory of samsung and LG.
difference is korean versions vs international models is korean may have a slightly different processor, which is usually faster and better than the international model, and they have an antenna which is for the korean national broadcasts.. both these are EXTRA features on top of the default world wide standard hardware.. so that makes them better in any case..
SCh and other code names are for international models, to be spold by carriers.. GT-i9300 is international galaxy model. SCH, and F-, VZW are codes for korean, or american or carrier models.. this is easily confirmed by searching your phone model on GSMARENA.com.. the codes are regional models are all listed on the top of the specs page. all those models are original products, just region based or carrier based.. specs changes due to region are also mentioned there
some old korean models of samsung had problem of korean language being the default and couldnt be changed, now majority new phones even korean models dont have that problem, or can have their language changed with simple rom flash.
CLon phones and MTK chip phones are FAKE< . not made by LG or samsung, made in china, and samsung sticker and casing put on it.. avoid at all cost.. they can be spotted by a lot of features easily.. google, "how to spot a fake clone galaxy" and you will find many sites with pics to clearly differentiate them
root is just a software feature. it has nothing to do with samsung or fake or korean.. it is a process which helps unlocks the advanced system settings which you can change in android software iteself, no matter which phone you use. some companies donot allow roting at al, but hackers always find a way. rooting helps change advanced settings, modify hardware functions and overclock etc.. it is also usually an easily reversible process, so you can simply Un-root with a click should you want to.