There are objective elements and subjective elements to morality. We can all observe the objective elements but only God knows the subjective elements. It is difficult to say with certainty that a specific person has committed a mortal sin because it requires knowing what is in his heart. However, we can say that something is a grave sin because that is based on observable actions. Abortion is always a grave sin. It is theoretically possible for it not to be a mortal sin.
This is what's confusing to me. How do "mortal" sin and "grave" sin differ? What does grave sin do to a person, vs. mortal sin? We know that mortal sin deprives a soul of sanctifying grace and sends them straight to hell. What does grave sin do? The same thing?
There two ways of considering sin, objectively or subjectively. When considering it objectively, we are thinking about the action in itself. To say that something is a grave sin is to say that, in itself, it is very wrong. We don't ask the question "what does grave sin do to a person" because asking what it does to a person means we are considering the question subjectively. It is like asking "Is celery your favourite fruit?" Celery doesn't belong in the question because it it isn't part of the category you are discussing.
Something that is a grave sin is potentially a mortal sin. If it is a mortal sin it deprives your soul of sanctifying grace. If it is not a mortal sin then it does not. For practical purposes, treat your own grave sins as if they were mortal and get to Confession as soon as possible. Other people's grave sins are rarely something you need to think about (although it is always a good idea to pray for people who are doing anything gravely sinful). There is not likely to be a reason for you to need to know if somebody else's grave sin is also a mortal sin.