I believe "ledger" implies commutative property (order does not matter).

I am not aware of any such implicit connection of ledger and commutative property, also couldn't find anything as my google-fu is letting me down. Anything I can refer to? Generally curious to know use of term ledger outside of accounting and blockchains.

I have seen it used to mean WAL before, so I am taking this with a dose of skepticism.

In a double-entry ledger the order of transactions doesn't matter, the balance is the sum of entries.

Depending on the data model of your log, if calculating the current state is a commutative operation, I think it's fair to call it a "ledger".

We called it a ledger since we stored financial data and basically used the “ledger” format from plain text accounting, initially.

That answers my question, thanks! Ordering does not matter part has me curious too, I will read other comment and come back to you l.