Ordinary כפרה (atonement) means with blood that is spilled. And any place where the atonement is not with blood - it will elaborate לכפר על נפשותיכם (to make atonement for your souls).

And we also find כפר with words that are a confession.

Numbers 31:50 says, ונקרב את קרבן יהוה איש אשר מצא כלי זהב אצעדה וצמיד טבעת עגיל וכומז לכפר על נפשתינו לפני יהוה*(And we have brought the LORD'S offering, what every man has gotten, of jewels of gold, armlets, and bracelets, signet-rings, ear-rings, and girdles, to make atonement for our souls before the LORD). In this case, the atonement was not with blood, so it had to elaborate “to make atonement for our souls”, in accordance with Rule 350⁶³⁶.*

footnotes: ⁶³⁶ Malbim, HaTorah v’HaMitzvah Vayikra 32.