Hey there; Those phrases refer to a user-made trading guide known as the Rares List (found here). The rares list is a list-style guide that's trying to put the most valuable pets on the site in an order from most to least valuable, so that people have a reference for how much they are worth compared to each other. (You can read up more on the specifics on the thread itself if you're interested.) Since the list is based nearly entirely off users' opinions and factors things such as a pet's popularity into their judgment it is in no way an official ranking of these pets' values or actual rarity, but it has nonetheless become a popular reference for trade fairness among the community.
There's two ways that "on/off list trading" can be read: "trading on(to)" the list would mean that someone is using non-list pets to trade for a pet that is on the list. "trading off the list" can mean that someone trades off a list pet for pets that aren't on the list. But it can also just mean that a trade does or doesn't involve list pets in general - "off-list" trades could just be any trade that doesn't involve the list, whereas "list trading" involves, well, list pets.
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