I've got a wireless ADSL broadband router at one side of a building,
but its signal is very poor at the other side of the building.
Therefore I need some sort of "repeater".

Let's say that the network I'm trying to get onto is as follows:
SSID: MonkeyBrain
Channel: 3
Network: 10.9.8.0/24
Gateway: 10.9.8.1

So far, I've heard of two kinds of technology for "boosting" the
signal.

Technology 1: You have some sort of wireless device that gets an IP
address on the MonkeyBrain network. This device then broadcasts its
own network with a different SSID, different channel, different
network. Let's stay that the new network is:
SSID: GorillaBrain
Channel: 8
Network: 192.168.1.0/24
Gateway: 192.168.1.254
When you send a packet to the internet from this new GorillaBrain
network, it goes to the default gateway on GorillaBrain, which
forwards it on to the MonkeyBrain gateway, which forwards it to the
internet.

Technology 2: I'm not sure how this works, but you can actually have a
device that just boosts the signal. You've got the same SSID, same
channel, same network address. You can communicate in Layer 2
protocols with the all machines on MonkeyBrain because you trully are
sitting on the MonkeyBrain network. I don't see how you don't have a
problem with both devices (i.e. the broadband router and the repeater
device) sending duplicate signals and taking in duplicate signals.

Which technology do you think is better? Which tends to provide a
faster connection? Are there any other good ways of going about
boosting a signal so that it's strong on the other side of a building?
(The signal I'm trying to boost is coming from an ordinary broadband
router that you'd get from an ISP, nothing fancy).

I was thinking of another way of doing it. Let's say that you have a
device which does the following:

Technology 3: You want to be on the MonkeyBrain network. You have a
wireless device that broadcasts an SSID such as GorillaBrain. It's on
a different channel to MonkeyBrain (let's say it's on channel 12), but
it has the same network address (10.9.8.0/24). When GorillaBrain
receives a frame on channel 12, it forwards it on to MonkeyBrain on
channel 3. In this fashion, you could have MonkeyBrain using WEP, and
GorillaBrain using WPA, but essentially they're the same network.
(e.g. if you went into the router statistics on MonkeyBrain then you'd
be able to see all the hosts that are on GorillaBrain, also all the
GorillaBrain hosts would get their IP address from the DHCP server
running on MonkeyBrain).

Is there any device the accomplishes what I describe in "Technology
3"?

Can anyone please give advice as to what kind of "repeater" device I
should get. My preference would be either Technology 3 or Technology
2. I think Technology 1 would introduce unwarranted overhead and would
add the complication of only being able to communicate via IP with
machines on MonkeyBrain.

Can anyone suggest devices, and perhaps give me an overview of the
technologies used? And don't be afraid to get technical, I've a decent
knowledge of datacoms (and also of wave transmission and the like).

Thanks for listening! :)

Tomás