Una corda on a grand moves the whole mechanism across so that the hammers hit fewer strings - one instead of two or three. Thus the name. In doing so, the volume is greatly reduced, at the expense of some sound qualitydifference.
The soft pedal on uprights does as you say, and brings the hammers closer to the strings, so they don't have so much of a swing before sounding the notes. A much cheaper and easier way to quieten the playing, but at the same time, still hitting all available strings.
The recovery time after a note has been played on a grand is less than that on an upright, so I'm guessing that because the hammers are even closer, that recovery time may be even shorter for the grand.
I really don't think there would be a necessity for a 'quiet practice' pedal on a grand, although the 4th pedal could be used as such. Mainly it'll be so that no quality of sound is lost, as all strings are still used, compared with pressing the una corda pedal. Or, if you like, there will be a subtle difference between the sounds of the soft and una corda pedals being used. And - imagine using both!