Exactly right.
SSID = Service Set Identification.
Since you’re wanting your “whole home” to be in the same Service Set, then setting the SSIDs the same does that.
This prevents your WiFi clients from having to switch profiles when they move from one AP to the other, which will also terminate any active connections (particulary with TCP-based protocols.)
Setting unique SSIDs will prevent clients from roaming until the signal gets so weak that they drop connection, then they might pick up the other one.
But the the ORDER of SSID’s defined on the client controls everything… If the weak one is on the top of the list, your client will always prefer it, even if the signal is barely usable.
