I don’t know. I can’t find anything that says Time Capsule/Airport defaults to Bridge mode.
I’m wondering if you ended up with an AirPort router where both sides are the same numbering scheme. If so, the results can be unpredictable. Certainly, whether the number schemes match or not, something on the WAN side of the Airport-as-router cannot see/ping anything on the LAN/Wifi side; while the LAN side of the AirP can see the Verizon device’s LAN. That sounds like what you were encountering.
Another test that you can do with a PC (on any LAN) is the DOS command “ipconfig /all” which will tell you what the DHCP server (source of address) is. I believe on an apple the command line is the UNIX command “ifconfig /all”. Can you print a status page to get all the printer’s setup details like DHCP server address?
If you are determined to make the device work…
I assume this is the one with 3 LAN ports, Wifi, and a WAN port.
Leave the Verizon device as the main router, as it is now.
Do NOT connect the Airport WAN. Connect only the LAn side.
Put it in bridge mode, i.e. turn off DNS and DHCP
Ethernet 201:
A switch is a multi-way bridge.
At Layer 2 of Ethernet, the one machine sends to the MAC address of another machine.
When the higher level functions require a packet to be sent to a particular address, it asks Layer 2 to send the data,
Local layer 2 - the source device broadcasts an “arp” which basically says “hello, who is x.x.x.x?” (Broadcast, to 255.255.255.255, because it has no idea what the MAC address is.)
The target machine replies with “That’s me” and tells the source its MAC.
The machine can now send a packet - [destination MAC][Source MAC][Data]
you can use “arp -a” on a PC to see the list of recent MACs it knows about.
If the destination is outside the local address range (based on subnet mask) the device sends to the default gateway instead. The gateway knows how to send it on.
The source device may have started by asking DNS what the IP address of a network name is.
A switch watches the traffic going by. Every packet it sees, tells it which wire which MAC address is on (remember packet includes source’s MAC). It builds a table.
It sends any incoming packet to all other connections at first - but as soon as it hears and knows a MAC address, it only sends (and only needs to send) the packet out that connection. (Broadcasts of course, go out all connections).
DHCP hands out default gateway as well as IP address (and subnet). Remember, all packets destined for outside the subnet are sent to the gateway.
You could connect to the Verison box or the Airport and whichever is/are doing DHCP, you should see a list of MAC addresses, device names, and DHCP information. This will tell you who is doing what.
So when a device is a router, it or some other DHCP server on the subnet (LAN) says “this is the default gateway” (and it knows how to pass the data on to the WAN port).
When a device is a “bridge”, it will pass a packet from one device to another but nobody thinks it is the default gateway, so nobody send it packets to be forwarded. But, since it hears all the other devices on the LAN side, it will pass packets between them all. If it is also Wifi, then Wifi simply acts like another network cable - it keeps track of MAC addresses it hears, and if a packet come in on the wires, and the MAC is wifi, it sends it out the radio; ditto, incoming wifi packets could be forwarded to wired.
if you don’t turn of DHCP but the WAN is not connected to the internet, then some devices will have the wrong gateway and send packets where there is no internet, and you will be able to see local but not internet from those devices.
If there are two DHCP on a network, then it’s luck of the draw or dueling device speeds who responds to address requests first.
When you make changes to DHCP, either reboot a device or unplug network cable for 10 seconds to force a new DHCP request for the new DHCP setup. Otherwise, the device will keep using its address until its lease is up - often 8 days.
Several options -
-if your printer was on the other side of a router than the MacBook, then the broadcasts (simplest way to find an unknown printer on what was supposed to be a local network) would not work.
-bridge mode supposedly turns Airport WAN port into a LAN port. (and turns off DHCP, on the assumption someone else is the router / gateway and DHCP).
-if you did change router setup, if the link to the printer did not go down (i.e. power of/on the airport) then it would have no reason to obtain a new improved IP address.
-the printer config (panel or print status page) would tell you IP, mask, and gateway which should tell you what to do.
-bad bad idea to have two DHCP on network unless configured not to overlap. they should also agree on the layout - mask, who’s default gateway, etc.