what Intell said
extend / join are an apple thing
extending / wds is not a wireless standard it is a wireless technology
and you need the same brands and models to work
the wifi alliance does not certify anything for wds
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knowing this
what you can do is run an ethernet wire from the FIOS modem to the airport
and call the airport a totally different wifi network. , giving it a different wifi network name and password
if you give your airport a totally different name, it will let you put the airport on a totally different channel
and your laptop, or iPad, will connect to whichever one it thinks has the stronger signal
you might be able to put the airport in bridge mode.
and the stuff connected to the airport router will have the same subnet mask as the other stuff in your network like "192.168.1.*"
if you do not put the airport in bridge mode then it might cause problems
because some stuff on your network will be "192.168.1.*" and whatever stufff connected to the airport will be "172.16.1.*" this is called double nat
if you put the airport on router mode, anything connecting to that airport will be double nat and it won't work if you run a web server or you have something at home that needs an incoming port like peer to peer file sharing
another thing you might be able to try is set an entry for the airport in the verizon fios router called "dmz" , where all the ports will be forwarded to the airport. sometimes that works with incoming ports like peer to peer
if you dmz from the fios to the airport , you can put the airport in router mode and it work and not double nat you
i have had some issues with apple and double nat. and found some things that we take for granted being able to do with apple , fails when you are double nat
i thought i would throw this out , before you take your airport back