To answer my own question: no, they use different pickups.
The CDZ's laser part number is: H8151AF
You can get them for $9-12 shipped on
aliexpress. Just check on the picture of the laser's label to make sure it's the real part made by Sharp.
Don't get scammed by gamedoctorhk, who sells them for $30-50 and obscures the pictures to hide the laser's part number.