Mark has the specific details of your setup, this is more a general response to help your understanding in general of home routers.

Your cable modem has one internet IP, and your router via it's internet port handles sharing that one address to your multiple devices. All your multiple devices lack an "internet" IP, and instead use IP addresses reserved for private use only.

It's like an apartment building. 123 Broadway St is the cable modem. The postmaster drives from the post office to 123 Broadway St via a road (ISP network). Then enters the building to go to the mail room (the router), and divides up all the mail into little mailboxes private to the building. A bill for apartment 221, some junk mail for apartment 312, and a legal letter to apartment 640 (Incoming traffic). In the outgoing box is a request for a Sears catalog from apartment 518 (outgoing request for Amazon.com). Each apartment is one of your devices attached to the router wirelessly or on the LAN ports. Each apartment shares the same street address and the mail room is the equivalent of NAT, a protocol the router uses to share the Internet IP/street address. Outsiders to the building have no idea how many mailboxes are inside that mail room.

By hooking into the internet port of the second router, internet traffic has to be delivered not through one mail room, instead now two. Lets say this is apartment 221. For some reason the apartment has a mail room inside it as well once inside the front door, and multiple locked rooms labeled A, B, and C. Mail now goes to a street address first (123 Broadway), then to the first mailbox for apartment 221, then to a second mailbox inside 221 labeled for 221-B.

Plugging into the LAN port bypasses the router portion of the secondary and treats any device connected to it the same as your upstairs router.

You may or may not want to have one shared private network between you and your neighbor. Which is independent of the choice to have one or two wireless networks.