Ethernet.begin(mac) returns 1 0r 0 so we can identify whether it is connected or not. But in case of Ethernet.begin(mac, ip) it is void method, so how to know it is connected to internet or not ?
Ethernet.begin() Initializes the ethernet library and network settings
in particular Ethernet.begin(mac) attempts to connect to a DHCP server to obtain an IP address etc - the function return indicates if the DHCP connection was sucessful
You determine if it connected to the internet by attempting to open a client connection or similar