Like so many things in this industry the point is establishing a shared meaning for all the humans involved, regardless of how uninvolved people think.
That being said, I find tying the level to expected action a more useful way to classify them.
But what I also see frequently is people trying to do the impossible and idealistic things because they read somewhere that something should mean X, when things are never so clearly cut, so either it is not such a simplistic issue and should be understood as not such a simple issue, or there might be a better more practical definition for it. We should first start from what are we using Logs for. Are we using those for debugging, or so we get alerted or both?
If for debugging, the levels seem relevant in the sense of how quickly we are able to use that information to understand what is going wrong. Out of potential sea of logs we want to see first what were the most likely culprits for something causing something to go wrong. So the higher the log level, the higher likelihood of this event causing something to go wrong.
If for alerting, they should reflect on how bad is this particular thing happening for the business and would help us to set a threshold for when we page or have to react to something.
That being said, I find tying the level to expected action a more useful way to classify them.