What is the difference between the AC mode and Router mode on Reyee EG?

In addition to the number of manageable devices between the AC mode and Router mode, you also can check the web-guide of Reyee EG for more details:
① Router Mode：
The device supports routing functions such as route-based forwarding and network address translation (NAT), VPN, and behavior management. It can allocate addresses to downlink devices, forward network databased on routes, and perform NAT operations.
In the router mode, the device can access the network through Point-to-Point Protocol over Ethernet (PPPoE) dialing, dynamic IP address, and static IP address. It can also directly connect to a fiber-to-the-home (FTTH) network cable or an uplink device to provide network access and manage downlink devices.
② AC Mode：
The device supports Layer 2 forwarding only. The device does not provide the routing and Dynamic Host Configuration Protocol (DHCP) server functions. By default, the WAN port obtains IP addresses through DHCP. The AC mode is applicable to the scenario where the network is working normally.  
In AC mode, the device serves as the management controller to access the network in bypass mode and manage the AP.