Your turbo compressor and turbine wheel look like this inside your turbo
there's a solid shaft that runs the length of the turbo and the wheel on the hot side is connected to it. on the cold side, the compressor wheel slides over the top and bolts to the other end of the shaft. when you wiggle one side or the other with your finger it'll move the whole shaft inside. So there isn't any bolts on the wheels themselves.
He's a breakdown of just the turbine wheel itself
In the first picture you can see the orange journal bearings on the shaft, those are where the shaft 'play' comes from. if the nut on the end of the shaft is loose, that's a different story entirely. But yes, the 'bolt' on the cold side should move a little bit from side to side and about ~.003" in and out. It should however feel completely solid with the wheel assembly. They shouldn't move independently from eachother.