When Windows is asking you about public/private/work it is asking which Windows firewall profile should be used for that network. Asking you about the firewall profile is necessary because a stock install of Windows will have many services running that are listening for incoming connections.
A typical Linux desktop install doesn't usually start any servers, or if it does these servers are limited to something like OpenSSH that requires strong authentication. Or the servers have the IP networking disable or they are bound to the loopback interface only.
Since there are no services listening for incoming connections, or at least very few the desktop firewall is not nearly as big of a deal.
If you do choose to enable a desktop firewall the firewall usually defaults to blocking all incoming connections by default and only permitting outbound traffic. If you want incoming traffic you have to typically have to take explicit steps to permit it.
Compare this to a domain/private firewall profile which may permit incoming services like SMB, remote registry, remote administration, remote desktop connection and so on. All these services with the correct authentication can be used to modify your system, and your data.
If you want to see the various settings Load up the Windows Advanced Firewall configuration.
