It does depend on your risk context. I tend to use "potential for fatality" as a rough guide, but it may be that "potential for serious injury or fatality" works more effectively.
It depends on what you are using the category for - be careful not to waste a lot of time arguing over category, rather than driving improvements. We report on all of our incidents by potential, rather than actual, so that the focus is on the degree of loss of control, rather than the outcome, which can vary according to good (or bad) luck. But we then add extra detail in the report for those deemed as 'high potential'

That's ta fundamental misunderstanding of the risk matrix. risks do not exist as a point on a 5 X 5 consequence/likelihood grid. At best they can be thought of as a line - high likelihood of a low consequence/low likelihood of a high consequence. Judgement needs to be used to select what a reasonable score is, and there should be some discussion with major risks. In the example you cited, it would require a series of events for a trip to result in death, but only one to result in minor injury. So stating that it is a 'catastrophic' risk is unreasonable.
Knowing which of these two factors is driving the risk value(s) is key to selecting an appropriate action.

As a simple guide, look at the worst case reasonably foreseeable outcome for consequence assessment. Catastrophising every event defeats the purpose of risk management as everything becomes high potential, low likelihood.
If you don't clearly define what is high potential, then you will not be properly prioritizing where to spend your limited resources.

I agree, looking to the worst case in every case blinds people to what they need to prioritise. I like to use the phrase "probable outcome". If the probable outcome is a life altering injury or death - that is "high potential'.

Our definition of an HPI: "is an event that could have or almost resulted in serious injury or illness causing permanent or temporary disability, irreversible health effect or fatality to 1 or more person or extensive damage to an asset". Event includes an incident, accident or near miss event. Asset includes network electrical asset, plant or equipment.