The actual piston-to-bore clearance as honed is specific to the piston being used.
Different types of pistons have different materials and expansion characteristics, and have diffrerent needs.
As for the top of the piston being able to be moved around by hand, that's because the top of the piston is much smaller than the biggest piston dimension. The biggest piston dimension is measured at the skirt, probably around the same height as the wrist pin, and measured from front to rear. That's where the piston-to-bore measurement is taken.
The top of the piston must be considerably smaller to allow for the rocking motion of the piston in the bore.
Proper running clearances at the skirt measurement are very critical, and must be precision measured with very accurate measuring tools.
Depending on the piston in question, it might need as little as .002" clearance, or as much as .006" clearance, or anything in between. And you have to get it right, or it will seize if too tight, or slap if too loose.
There is no "guesstimation" allowed in this area. You have to know exactly what to do.