Chances are, it will be the SSD itself. It is possible to be the controller but very rare for it to happen. SSD cards are unreliable and a lot of people have reported on "Drive C:" vanishing.
You are at the recovery point which was displaying the base drivers of Windows when you originally tried to perform the recovery and explains why no drive was available.
The SSD card needs to be replaced but not practical with these tablets. If the machine is still under warranty, contact Microsoft Customer Support to see if you can get the machine swapped out.
As for a difference in controller, not much. The two tablet models are built differently but the controllers are usually generic.