So mesh nodes can be Router/Gateway/Hub/Switch/WiFi Card, connected by cable
this is where the confusion is , true mesh topology is where the ap's are not connected by ethernet and connect to each other and to a main router or ethernet via wireless alone , you can think of it a bit like the old WDS system although its not that similar
open-mesh have been doing the concept for a while now
http://www.open-mesh.com/
so yes its a topology where the ap's form a collective and become one mind ( a bit like the borg re star trek ) thus allowing the client devices to roam without disconnection and seamlessly while the backhaul is passed between ap's to get to the primary point which is connected by ethernet
in the amplifi blurb it states
Amplifi works by creating a mesh network rather than by "extending" Wi-Fi. Traditional Wi-Fi extenders (along with repeaters) re-broadcast your existing Wi-Fi signal on a second SSID, effectively halving the available client bandwidth. In a mesh network, each network component uses some variable chunk of its bandwidth as "backhaul" to talk to other network components, and the rest to talk to clients. The network components also all share the same SSID, and clients can roam freely between them.
the last bit is not technically correct as they have the same bssid but i guess that would confuse things
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so there is certainly a difference in what some claim to be mesh topology and what real mesh topology is
imho to be a true mesh system the ap's can work with or without ethernet backhaul , they communicate between them selves to become one big single entity as far as any client device is concerned
whereas if all ap's only communicate back to the main router via wifi its star topology