Perhaps the same task but I would venture to say that the sensors and motor movements required to balance on a "flat" "friction" surface are different than those required to balance on a "frictionless" one (good call there, Jamt!). We need to train our bodies to make different correcting balancing movements when we have the ability to move our feet (BoS) to "capture" the balance of the CoM than when we walk and move our CoM to place it over the BoS.
Might differing signals of unbalance also occur when we lose our BoS, our feet slip? Certainly our reaction to it in the normal walking world is rather dramatic and quick, our hands fly up and we do whatever we can to get that CoM back over our BoS.
Balance is a learned skill. How you become unbalanced and what you can do to regain it varies with the activity. It is also a bit more than just regaining balance, but regaining it in a manner that allows you to continue the activity.