Is there a difference between total-ordering consistency and linearizability?

Question

By total-ordering I mean the following definition[0]:

Total Event Ordering: Controller replicas should process events in the same order and subsequently all controller application instances should reach the same internal state.

If my understanding is correct, there isn't any difference and the two words can be used interchangeably. However, I would like to make sure I am not mistaken.

In the case both concepts are different, could you stress their differences and perhaps provide an example? That would be very much appreciated!

Thank you,

[0] - https://www.cs.princeton.edu/~jrex/papers/ravana15.pdf