The Kimetsu no Yaiba wikia refers to the Dance of the Fire god breathing and to the sun breathing as if they were the same breathing several times, and if they were different breath styles several times. For example, in these quotes it refers to it as if they were different,
he realized his own Hinokami Kagura (dance of the fire god) had unncessary movements, different wrist angles, footwork and breathing rhythm. Removing them enabled him to awaken the legendary Sun Breathing
Both the Hinokami Kagura (dance of the fire god) and Sun Breathing are Breathing Styles that mimics the sun and replicates it with the user's movements, techniques and abilities
However here, it refers to them as if they were the same,
The Hinokami Kagura (dance of the fire god) is later revealed by Shinjuro Rengoku to be a legendary Breathing Style known as Sun Breathing
Hinokami Kagura (ヒノカミ神楽かぐら Hinokami Kagura?, lit. Dance of the Fire God) is a Breathing Style only known and taught by the Kamado Family, later revealed to be the first Breathing Style, Sun Breathing
So, are they different or are they the same?
Is there any difference between the Dance of the Fire god breathing and the sun breathing?