https://wccftech.com/guide-call-of-duty-black-ops-cold-war-ps5-120hz/

The PlayStation 5, unlike the Xbox Series S|X, treats the PlayStation 4 and PlayStation 5 versions of the same game as different titles. This is great for trophy hunters to get twice the unlockable achievements, but if you're just wanting to get into the game as quickly as possible or have a metered data connection, you don't want to run the risk of downloading the PlayStation 4 version of your latest game. Today, we're doing to show you how to ensure that you're going to get the PlayStation 5 version of Call of Duty Black Ops Cold War as well as enable the hidden 120Hz feature you probably didn't even know about.

For starters, this is going to assume that you own the Cross-Gen digital bundle for Call of Duty Black Ops Cold War. If you have the PlayStation 4 version on disc, you will need to purchase the $10 Cross-Gen Bundle upgrade that unlocks the PlayStation 5 version (Xbox One takes advantage of Smart Delivery to get around this).