Both kinds of pedal are typical, but it depends on the type of piano. For uprights, the una corda pedal moves the hammers closer to the strings so they don't a

Both kinds of pedal are typical, but it depends on the type of piano. For uprights, the una corda pedal moves the hammers closer to the strings so they don't accelerate for as long on their way in. But on a grand, the una corda pedal indeed still shifts the entire mechanism to the right so that the hammers truly hit una corda each.