Linked products are the same exact product displayed in 2 or more categories... A product has one master_categories_id therefore when "viewing" the linked product the master_categories_id applies to all showings of the linked product's master_categories_id...

Therefore if you link the product to the category(ies) then change the master_categories_id on any of the representations of that product it changes "everywhere"... But if you copy instead of link... Then the copy is it's own "animal" and modifications made to the copy stay with that copy and any linked product off of that copy.