At the moment, I have the BT Smart Hub SSID, and a seperate SSID for a TP-Link Wi-Fi extender.
Having two SSIDs is messy, as devices don't always switch between them.
If I removed the TP-Link Wi-Fi extended and added four BT Mini Whole Home Wi-Fi discs to the network, how many SSIDs would there be?
Obviously it's personal preference, but I consider separate SSIDs better as the source of the signal is known and a manual force to a stronger signal can be achieved.
The whole home discs are a mesh system and will have one SSID. It is usual to turn off the router WiFi when using the discs as it doesn't form part of the mesh. If it remains active, you will have 2 SSIDs.
If you would prefer just 1 SSID, then provided your SH and TP-Link are wired together by ethernet you should be able to set the TP-Link to have the same SSID and Pwd as your SH. You would then have just one wireless network and should be able to move between the APs seamlessly.
Giving APs the same SSID doesn't provide seamless roaming between them, mesh capability is required for that. A common misconception.
Poor choice of wording on my behalf I agree, what I meant is that no action would be required from the user to connect to either AP (router) and that switching would occur automatically if needed (due to loss of signal from the current AP in use). Both APs would also need to implement the same security WEP(!), WPA, or WPA2
Seamless roaming would be possible if both APs supported seamless handoff though that is not very likely without enterprise level APs.