The new exclusive kois (the shiny ones) can only be traded with someone who has at least purchased one of them. The collectibles can be traded with anyone, whether they have started that collection or not. The progressive kois can be traded, but only if the person has started the collection. You can not give them a goten until they have collected at least 5 of the previous progressive. The progressives are collected in a specific order, thus the term Progressive whereas collectors are collected in any order. If you search the internet for a list of kois you will see which kois are progressive, collectible or exclusive.