Wifi Access points VS Bridges

[shay walters]

I seem to have some sort of misunderstanding about what's going on
with my home network. I have the main house and two out-buildings.
My internet service in the main house comes in on a Wifi router (No
wired access available - Visible.com - the router has WiFi uplink as
well as WiFi downlink, no wired connection) That WiFi router connects
through Wifi to a Wifi Bridge, which then serves the wired devices in
the house, one of which is an AP that serves the two out-buildings.
In each out-building, I have a Wifi bridge which serves the local
devices. In one building, that bridge is wired to an access point
for local Wifi connections.
I've occasionally had odd connectivity problems (device A can see
device B, but not the other way around, for example.) When I first
hooked this all up, everything was working, but it has gotten
progressively more squirrelly over time. Recently, I installed a new
internet service. The old service is still active. But it was around
this time that everything in the old setup went south. I want to
switch everything to the new service, but I want to understand where
I've gone wrong on the existing setup before I repeat the mistake.
Is there a good reference site that explains when to use a bridge
rather than an AP? (The devices I have can be configured for
either.)

Thanks in advance,
-Shay