Aren't they both descendants of the same family line?
Mist Hashira's father has the same eyes as Tanjiro and his crow also mentions that he is a direct descendant of the guy who invented the first breathing style.
Maybe the mark is related to just the bloodline. Or it's related to demon-slayers in general, considering all the breathing techniques are sub-techniques of the first one. Maybe it's a "I'm in the zone" thing.
They look a little different as well. Mist Hashira's is a bit more "flowy" and reminds me of clouds.