I’m guessing they use the motorized wheelchair for traveling longer distances and the stick for walking into inaccessible areas or when it’s more convenient to do something while standing. As for how they’re using it, I’d guess it’s just a way to carry it with them in the chair since holding it horizontally on their lap might hit people that don’t see it, and it is easier to perform that motion than to hold it steady in some other, more awkward position.