Comment by arghwhat

A network where every node has a direct connection is a point-to-point network. Yes, it is a special-case called a fully-connected mesh, but these networks are rarely made (a fully-connected mesh of 32 servers require 32 NICs in each server and 496 cables) and it is not a common term.

What is usually described as a mesh network (technically: "partially connected mesh") is a network where every node has a route to every other node, and that every node may have a direct connection to any number of nodes, but where there is no guarantee that any two nodes have a direct connection and may need to route over other nodes. The ability to handle this sort of completely arbitrary network topology is the core to mesh networks.

See https://en.wikipedia.org/wiki/Mesh_networking. There's also the old WiFi mesh spec (https://en.wikipedia.org/wiki/IEEE_802.11s, what the OLPC used), not to mention Zigbee and Bluetooth Mesh.