In some places (like Mishlei 3:3 and 7:3) our hearts are compared to luchot (tablets) on which one should inscribe the words of HaShem.
In another places our hearts should be circumcised: Devarim 10:16, which seems to be about cutting off our evil affections, and Yirmiyahu 4:4 (see also Devarim 30:6), where it means to remove wickedness.
In yet other verses (like Ezekiel 11:19, 36:27) it says the heart of stone will be replaced by the heart of flesh.
Rabbi Levi in the name of Rabbi Hama bar Hanina said: "G-d’s laws are called hukkim because they are engraved (hakukim) as a safeguard against the Yetzer Hara (the evil inclination)." Rabbi Levi elaborated: "This can be compared to an outpost threatened by brigands. What did the king do? He sent a guard to protect it. So, too, the Holy One Blessed be He said: The Torah is a rock and the Evil Inclination is a rock. The Torah (a harder rock) will defend against the Evil Inclination (a less hard rock) – "I will remove the heart of stone from your body."
All of these seem to talk about our hearts, the words of Torah which should be on them, and the evil inclination which should be removed from them. So what I would like to know is:
What's the difference, and what is the common denominator, between a heart that needs to be engraved/written on, a heart that needs to be circumcised and a heart that needs to be transformed into a heart of flesh? And what should one learn from this?