The IP detected by this page is the public IP and not the private IP, because from the outside it is not possible to know the assignments made by the router in the local network.
An IP address (Internet Protocol address) uniquely identifies a device connected to a computer network. An IP address identifies a specific computer or other device within a network. IP addresses can be assigned locally to create a LAN (Local Area Network), IP addresses can change their value depending on many factors (different LAN, dynamic addressing) or by user choice. An IP address is assigned to an interface that identifies a network host, a personal computer, a smartphone, a router, or appliances in general. It must be considered, in fact, that a host often contains many interfaces, for example: a router has different interfaces and for each one an IP address is required.