Check the BSSID, that is, the access point's MAC address.
At home you'll usually have only one access point that's built into your router, so compare the MAC with the one written on the sticker on its bottom. (It might differ by a single digit in some cases.)
You didn't mention the OS you use, so I'll assume Linux:
$ iw wlan0 link
Connected to 24:a4:3c:ce:d2:16 (on wlan0)
Or you could check whether a scan detects multiple APs with the same name:
$ sudo iw wlan0 scan | egrep "^BSS|SSID"
$ nmcli -f in-use,ssid,chan,bars,security,bssid dev wifi list
There are various "Wi-Fi scanner" apps for Windows and macOS as well – can't recommend any, but most of them are able to display a basic "network list" including channels, BSSIDs, and all that. There's one from Nirsoft, and probably heaps of other freeware.
If you're on Windows (7 or later), the same can be done via
C:\> netsh wlan show interface
There is 1 interface on the system:
SSID : eduroam
BSSID : 24:a4:3c:ce:d2:16
Network type : Infrastructure
Radio type : 802.11n
(I can't remember offhand what's the command to request a scan, but it's also under
netsh wlan show <something>.)
On macOS, this post suggests:
/System/Library/PrivateFrameworks/Apple80211.framework/Versions/A/Resources/airport -I en1
link auth: wpa2-psk
MCS: -1 channel: 6
On FreeBSD, all that should be under
Android has quite a few "Wi-Fi analyzer" apps; at the time of posting, this one worked well.
The homepage, however, is not a network setting. Only your web browser cares about that.