Fun fact: Seraph and Seraph with a Live Coal are not listed under generic characters, while both versions of Seraphim (from Warriors) are. I'm not entirely sure if that's the way it should be, but I think the most-up-to-date ruling is this:
In a 50 card T1 deck, you can have:
1 of Seraph and Seraphim (band to green)
1 of Seraph with a Live Coal and Seraphim (band to blue)
Since the Seraphim cards are both generic, then you can have any number of them in play at the same time, along with 1 Seraph and 1 SwaLC. I know SwaLC was made unique purposefully, but I'm not sure about Seraph, that may have been an oversight.
It's probably a good idea to have a discussion on why the two non-Warrior versions were made unique, if that is necessary, and nail down whether they are the same card as the warrior ones. I feel like we had a discussion on this awhile ago, but I don't think we ever came to a consensus.