What a repeater does:
A repeater should essentially:
- Grab the signal you point it at and simply repeat it
- Not be broadcasting its own SSID
You will need to tell it which signal, or SSID, to repeat. Clients will not be "connecting" to this repeater; the repeater will be boosting signals for them.
What a WAP with same SSID does:
What you're describing sounds more like adding another wireless access point (WAP) to your network.
- WAP broadcasts an identical SSID
- Clients choose access point based on signal strength
If you add a WAP to your network and use the same SSID, clients will choose (roam) between the two access points depending on signal strength. It's important to realize that the client does the math on which WAP to use.
You will have to add the WAP to your wired network however.
What WDS does:
To create another WAP wirelessly, you would need to set up a wireless distribution system (WDS).
- Functions like a second WAP with identical SSID
- WAPs/routers are aware of each other
- Can create a mesh network, bouncing signals off multiple
Expensive (for good reason) proprietary solutions exist, and work well. You can also set this up using DD-WRT and some good matching routers yourself. It's not user friendly to set up.