I have a problem with two other IP addresses. Whonix-Workstation shows a different IP than the Gateway? Is it obliged to be this way?
My host OS is Kubuntu, and on it I have VirtualBox running whonix-gateway and whonix-workstation. The loaded Whonix-gateway shows a different IP than whonix-workstation. Should these two systems (gateway and workstation) not be associated with same IP address?
Your two Whonix VMs should NOT have the same IP address, the Whonix gateway should be able to see its own external IP address simply because it has to connect to the internet to do its job; however, the Whonix workstation should never be able to find the public IP because its only connection is to a second (internal only) IP of the Whonix gateway.
It's not clear what IP addresses OP is referring to.
The Whonix gateway has two adapters. One adapter (eth0) may connect to the VirtualBox host, or to a router VM. It will report (using ifconfig) whatever IP address the corresponding DHCP server gives it.
The other adapter of the Whonix gateway (eth1) connects to a VirtualBox internal network (by default, "whonix") which it shares with the workstation. The gateway and workstation (obviously) have different local IP addresses on that internal network. By default, the gateway is 192.168.0.10, and the workstation is 192.168.0.11 (both static).
As adrelanos notes, Whonix uses stream isolation, so each isolated application will have a unique public IP address via Tor. However, because the workstation connects through the gateway, particular applications running on either should report the same IP address at any given time, until the circuit changes.
Firewall and routing rules on the gateway prevent local applications from accessing anything via eth0 except through Tor.
