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"Web of Trust" predates Cryptocurrency / Blockchain by decades.

Web of trust just means "If A trusts B, and B trusts C, then A trusts C." Nothing to do with distributed databases/ledgers.

Blockchain refers specifically to a linked-list-like data structure which utilizes cryptographic hashes at each node to store an authentication of the tail of the list on each head (node). If you have a similar structure using trees, it's a merkle tree. Replication + message signing does not imply either (necessarily).