If they're fully spinning it out, it isn't just "under the same parent company". They can make two companies each with their own stock, initially distributed to

If they're fully spinning it out, it isn't just "under the same parent company". They can make two companies each with their own stock, initially distributed to shareholders of the initial company. After that, some stockholders might buy/sell shares of company A and some might buy/sell shares of company B, so that they're truly separate companies with different management and owners and such.