[clarry]

> Clients therefore initiate communication sessions with servers which await incoming requests.

Dogs walk on four feet, therefore anything that walks on four feet is a dog?

> Both client-server and master-slave are regarded as sub-categories of distributed peer-to-peer systems.

Dogs are canids, that doesn't mean all canids are dogs.

The client-server model really entails more than having one party that sends a packet before the other. Some illuminating details and a shallow comparison to the peer-to-peer architecture can be found in the article you linked.