The Chatas and the Olah
There is a difference in halakhah between how a bird is slaughtered when brought as a qorban chatas and when brought as a qorban olah.
The Torah says (Vayiqra 5:8-10) that the kohein must “וּמָלַ֧ק אֶת־רֹאשׁ֛וֹ — flick off its head” of the bird offered as a chatas. But there is no similar instruction for the olah; it is just offered “כַּמִּשְׁפָּ֑ט – as the usual law”, shechted. The head is to remain attached.
The chatas atones for committing a sin, for violating a prohibition. Thus its name.
An olah atones for inappropriate thoughts.
Perhaps the point is that because a chatas represents letting one’s thoughts cause sinful action, the atonement requires disconnecting the bird’s head from its body.
The olah, however, atones for someone letting their thoughts disconnect from reality. So the kapparah requires keeping the head attached.