Apple stock was up more than 1 percent, trading above $117 midmorning Tuesday, while Samsung was down more than 8 percent. Apple shares ended the day slightly higher at $116.35.
Samsung said it would halt production of the Note 7 after several reports said that the phones would suddenly catch fire. Major smartphone carriers, including AT&T and Verizon, are allowing customers to exchange Galaxy Note 7s for another device, including Apple's iPhone.
Some investors think Samsung's woes could potentially boost sales of Apple's iPhone. Apple's stock is already reportedly up 20 percent over the last three months, which includes the time of the iPhone 7 debut.
In addition to market movement, Samsung and Apple will also be giving final arguments in a long-running design patent dispute today in front of the Supreme Court. The justices will be considering how much Samsung owes Apple for infringing design patents on Apple's iPhone with a final decision expected by late June.