Webi don't say that hinokami kagura is way weaker than sun breathing, but there are definitely some difference between them:

The hinokami kagura is a dance sumiyoshi kamado made.

Dance of the fire god) is a breathing style only known and taught by the kamado family, later.

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Dance of the fire god) is a breathing style only known and taught by the kamado family.

Websun breathing (ๆ—ฅใฎๅ‘ผๅธ , hi no kokyลซ) or referred as hinokami kagura is a style of swordsmanship utilized by yoriichi tsugikuni to use breaths, homura hino and serves.

Yoriichi is the fire god that the hinokami kagura (dance of the fire god) refers to.

It is passed on from.

Yoriichi showed sumiyoshi all 13 forms of sun breathing which he then committed to.

The user spirals into the air before coming down and delivering a deadly slash.

Webhinokami kagura (็ซ (ใฒ) ใฎ็ฅž (ใ‹ใฟ) ็ฅžๆฅฝ (ใ‹ใใ‚‰) , hinokami kagura?, lit.

Webthe hinokami kagura (ใƒ’ใƒŽใ‚ซใƒŸ ็ฅžๆฅฝ ใ‹ใใ‚‰ hinokami kagura?, lit.

Webthe hinokami kagura and sun breathing are two different things.

Webto bring it all together and answer your question, no they are not the same, but they are very similar.

Webits existence only remained in the form of hinokami kagura as tanjiroโ€™s ancestor, who was a close friend of yoriichi, memorized and handed down the sun.

Very closely related mind you, but they are different.

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