A repeater repeats the AP communications and wireless clients can talk to the repeater.
An AP in wireless client mode will talk to the root AP but wireless clients cant talk to the AP in wireless client mode. If group 2 is not going to use any wireless devices then the AP in client mode would allow them to communicate with group 1 through the Client Mode to AP path. As was mentioned, some APs in client mode will only bridge one MAC address and only one computer can talk. If you have group 2 on a router connected to the AP client then this is not an issue.