You can use the same wetsuit to surf or dive. No problems there.
Of course, the surfing wetsuit will start to fall apart very quickly after you’ve been diving with it for a few months. You see, neoprene can be made to be flexible and stretchy or it can be made to be tough and resilient. Unfortunately, it can’t really be made to do both at the same time.
The neoprene for the surf wetsuit is made to be very flexible and stretchy in order to accommodate the surfers active sport. The draw back to that flexibility is that the walls of the bubbles are not very strong. After they get compressed and expanded a few dozen times, the bubble walls will start to break down. Once the break down occurs, there’s nothing that will stop it and the insulation characteristics of the suit drop like a paralyzed falcon.
By the same token, the wetsuit made for diving will stand up to a few years’s worth of compression/expansion cycles before degrading. On the other hand, the suit won’t be very flexible to allow the surfer to do much in the way of fast movements necessary to ride a wave.
Ian