A creature's power and toughness aren;t counters in and of themselves, they are characteristics of the 'Creature' card type. From the Comprehensive rules, ad 302:
302.4. Power and toughness are characteristics only creatures have.
302.4a A creature’s power is the amount of damage it deals in combat.
302.4b A creature’s toughness is the amount of damage needed to destroy it.
302.4c To determine a creature’s power and toughness, start with the numbers printed in its lower right corner, [...]
These can then be altered using enchantments, instants, sorceries, abilities of sources such as other creatures or planeswalkers, and artifacts/equipment. Most of these effects are temporary in that they only last until end of turn (Giant Growth, or while the source is in play (Glorious Anthem). And sometimes this boost is done using counters which stay with the permanent when its source leaves play (Bond Beetle).
Counters are governed by their own set of rules:
121.1. A counter is a marker placed on an object or player that modifies its characteristics and/or interacts with a rule, ability, or effect. Counters are not objects and have no characteristics.[...]
In conclusion, you can only move a counter from a permanent when that counter is there in the first place, and base P/T are not counters.