In the official subs, 'Child of the Watch' is capitalised. It seems like a real title. I also seem to recall that in the flashbacks of our protagonist being found, the Mandalorians saving him are Death Watch. Given that the Empire has apparently fucked over the Mandalorians in some pretty horrid way, I'd say that their whole society is even more fractured than before, and they exist only in some kind of diaspora now.
Deathwatch probably fell apart after the Maul debacle, with the Children of the Watch being an ultra-traditionalist splinter group that retains identity and cohesion by stressing rigid adherence to the (real and/or imaginary) "traditional way" of their people.
Meanwhile, Bo-Katan had already separated her own little club (the Nite Owls) from Death Watch due to Maul killing Pre Vizsla and taking over. By the time of the Siege of Mandalore, she seems to have mellowed out, compared to her earlier radical stance. Her changing views (and her goal of uniting all Mandalorians) give her personal reasons to dislike isolationist splinter groups.
I wonder if there are more factions, or if they're going to simplify it to just these two groups.