Do All Nodes Have an Identical Mempool?
No, not all nodes have an identical mempool. While transactions are broadcast across the network, the mempool is a local cache maintained by each individual node.
Differences arise because of network latency, different minimum fee thresholds set by node operators, and the potential for transactions to be broadcast to different subsets of nodes first. However, the goal is for all valid, high-fee transactions to eventually propagate widely.