A carve-out raises cash and puts a public price on a unit, unlike a spin-off, which distributes shares and raises nothing. The parent typically retains 80% or more so that a later tax-free spin-off of the remainder is possible.
The float after a carve-out is tiny, which produces exaggerated moves and sometimes an implied value for the parent's stake that exceeds the parent's whole market-cap.
Example: a parent sells 15% of a unit at a $20B valuation, raising $3.0B. Its remaining 85% is implied to be worth $17B. If the parent's own market cap is $15B, the market is valuing everything else at less than nothing.