A repeater uses wireless in both directions - first, to receive some traffic from the far AP, then to transmit those packets to the local PC. Since the same channel is used for both actions, throughput is cut in half. (Actually worse than that, but whatever.) This happens at Layer 2, meaning both ends are on the same subnet when using a repeater.
dd-wrt's client mode and client bridge mode both bridge a wireless signal to a wired signal, if I remember correctly. So neither of those modes acts as a repeater.
The primary difference between client bridge and client modes is that client bridge connects the radio directly to the switch while client mode inserts the router section between the radio and the switch. Client bridge means both distant ends are on the same subnet while client mode (because of the presence of the router section in the path) means the two distant ends are on different subnets.