Move transaction script

I understand that a move script is executed by a client to invoke a move module on the chain. The question is that does the move script also executed by each node or just only that node who ran it. in comparison with ethereum when a smart contract is executed its executed by all nodes through EVM. I think the move module will be executed by each node through MVM as a smart contract but the transaction script that invokes a move module would not, its a local, single-use type of program for only that client who ran it first? move module execution results in a state change, whereas move script is just. an “invoker” which is not executed by every validator, just the client who ran it first? is this correct? thanks!

The question is that does the move script also executed by each node or just only that node who ran it. n comparison with ethereum when a smart contract is executed its executed by all nodes through EVM

The script is also executed by each node, the same as in the EVM. A transaction script is logically equivalent to a single transaction EVM transaction that publishes a contract C, calls C.main(<args>), then deletes C.