You can either connect it as a router or as AP depending if you wanted the same IP block or different. The recommended configuration is to run as a AP to simplify the network and things like port forwarding.
The SSID itself mostly is used to select the hardware you want to connect to it is only somewhat related to the network and ip you use. Some people prefer to use the same SSID and let the computer select the strongest signal and other prefer to control the device they connect to manually and use different SSID. In most cases they map the SSID to the same exact network.