Do I want a Repeater or a Bridge? (OpenWrt)

The two options are similar.

1. Bridge

   This sets up your device so that it bridges traffic between the ethernet interface and the wireless interface. Nothing more. Nothing less. Your ethernet interface needs to be connected back to the rest of your network so that wireless devices connecting to the Access Point can see your network. If you have multiple Access Points configured as bridges they all need to have an ethernet connection back to the same point. To allow roaming transparently between them they must all use the same SID but should be on different channels.

2. Repeater

   This sets up your Access Point so that it listens to another AP and re-broadcasts what it hears. It also acts as an Access Point for local wireless devices and then rebroadcasts the traffic back to the other AP. There is no wired connection to your network, so a Repeater can be installed anywhere within wireless range of another connected Access Point. The disadvantage is that the presence of a single-radio Repeater on your network will halve the wireless throughput. Typically such a Repeater will have to use the same channel as the Access Point to which it's paired. Newer Repeaters can listen and transmit simultaneously so throughput is not significantly impaired.

If you have a single Access Point connected to a router in a home scenario then you want Bridged mode.

If you need multiple Access Points, the primary one will always be Bridged. The additional devices will either be Bridged APs or Repeaters. Of choice, if you can run an ethernet cable (or powerline) to the secondary device(s), I'd go for the bridged option every time.