The difference between the heart قلب and the breast or chests صدور in Quran has been discussed by many scholars of Tafseer. We see some non Shia scholars claim that there is no difference between heart and breast. We can not accept this opinion because of the clear mention of hearts and breasts in the same Quranic verses which must mean a difference in the meanings.
Among many opinions, we can say that the breast or chest is wider than the heart and it is effected by the state of mind and feeling of comfort or discomfort. That is why we read the supplication of prophet Moses (AS): O my Lord, extend my breast (Taha: 25).
The heart is our inner which is the origin of our intentions, while the breast is effected also by outside reasons and factors which make us feel comfortable or otherwise. That is why we read in Sura Al-Inshiraah how Allah (SWT) tells His Prophet Muhammad (SAWA) mentioning His bounties on him: Did not We extend your breast? ألم نشرح لك صدرك which means that Allah (SWT) Has granted him this bounty of making his breast big and extended.
In Quran we read about Quran that it is : Cure for what is in the breasts وشفاء لما في الصدور (Younus : 57). What is in breasts can be a mixture of our feelings and our thinking and reactions to other factors surrounding us.
No doubt, heart is the Centre of the breast (Hearts inside the breasts) (ولكن تعمى القلوب التي في الصدور) )(Verily, it is not the eyes that grow blind, but it is the hearts which are inside the breasts that grow blind) Al-Hajj : 46.