But, what is exactly a bitcoin node ?
Is it a client like Bitcoin-qt or is it only a miner ? Or both ?
Bitcoin node refers to a "full" client. A "full" client is a client that owns the block chain and that is sharing blocks and transaction across the network. In opposite a Lightweight client can not be considered as a node because he doesn't share the block chain with the network.
Bitcoin network uses a client to client network infrastructure so there is no difference between a mining client and a non-mining client, they don't have any privileges.
"Node" refers to any computer that's running Bitcoin client software and participating in the peer-to-peer network by relaying transactions and blocks. It could also be mining, but it doesn't have to.
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