Removing a shield counter in this way isn't the same as regenerating a creature.

A creature with a shield counter on it may still be destroyed by state-based actions if it has damage marked on it equal to its toughness or has been dealt unpreventable damage by a source with deathtouch.

Combat damage is assigned to creatures and players and then dealt simultaneously. Notably, this means blocking a Rhox Pummeler with a shield counter on it won't normally prevent Rhox Pummeler from dealing damage to the defending player due to its trample ability.

If an attacking Rhox Pummeler with one shield counter on it is blocked by a creature with first strike, the shield counter will be removed in the first combat damage step. In that case, Rhox Pummeler won't have trample when it deals combat damage in the second combat damage step.

Shield counters don't prevent players from sacrificing creatures.

"Shield" is not an ability that creatures have and shield counters are not keyword counters. If a creature with a shield counter loses its abilities, the shield counter will still protect it as normal.

If a permanent that would be dealt damage has more than one shield counter on it, that damage is prevented and only one shield counter is removed.

If a permanent with a shield counter is dealt unpreventable damage, that damage will be dealt and a shield counter will still be removed.