A split-off is an exchange offer rather than a distribution. Holders choose whether to swap, so unlike a spin-off not everyone ends up owning the new company. The parent retires the shares it takes in, which reduces outstanding-shares the way a share-buyback does.
The exchange ratio is usually set at a discount, often 7% to 10%, to encourage participation, and is frequently capped so heavy demand leads to proration.
Example: a parent offers $107 of subsidiary stock for every $100 of parent stock tendered. Tendering 1,000 shares at $50 gives up $50,000 and receives $53,500 of the subsidiary, subject to proration if the offer is oversubscribed.
Related: spin-off, carve-out, tender-offer, outstanding-shares