I believe they're implemented as follows to simply summarize
Public protects your device from being identifiable on the network, Imagine your pc is in a public space do you really want people to find your device easily, potentially attacking your device or accessing features of it?
Home/Private:This device is used on your personal home network therefor you trust all the devices present in it as such you allow devices to be able to take advantage of features such as Mapping drives or creating Homegroups.
Tbh if you're not going to make use of any features offered in the Home network it is not worth considering and you should always opt for the Public option, as soon as you wish to make use of the features of Private you can switch this yourself from your control panel options.