I think that we're each using a different definition of "understanding."
Mr Literal over here meant understanding the nature and state of the person, which too can engender connection.
But I don't have a Buddhist view, only a Boogist view!
As I see it (also, as a Buddhist sees it) all things are transitory and in a constant state of change.
And as I do too, but again I suspect at a different level, in fact it's at the meeting point of chaos and order that things really happen, the change from low to high entropy and movement from simplicity to complexity (and back to simplicity).
A person overcome by fear (for example) feels, at that moment, great fear. If another, through empathy, also feels that great fear, that is understanding what that person feels in that moment.
Or believes they do? I'd say that fundamentally this can't be done in any absolute sense.
So to your point, it's not just the word 'understanding' that's lacking a common definition, but also our definition of 'empathy', which can sometimes mean you
believe you understand their feelings and other times that you
do understand their feelings. And there are other definitions too, so
we're not really connecting here!
You may think you know someone for years, and they may end up being a completely different person than you imagined.
Yes indeed!
I've noticed this phenomena and for a lot longer than I've known anything about cognition and related matters (the subjectivity of perception). But I came up with a strategy for it a long time ago and a lot of it centred around the concept of trust.
Trust (for me) is fundamental to anything coming close to a real friendship, and because people are far more complex and nuanced than many consider, when we think we may know someone well, the reality is we've only seen small portions of them, and what comes out of them isn't necessarily what's inside. So I realised it was never possible to truly know someone, and it's very likely this is for the best (in this culture).
So I measure out my trust in small portions to start with, only that which I'm willing to lose. As my small bits of trust are rewarded, I'll trust a little bit more, and so on. This of course doesn't protect me from being 'betrayed' in some way (having my trust used against me), but it's helped to rationalise and set limits, and understand when those limits have been crossed, so the blow isn't as painful. I'm not left in anguish wondering what happened and how, just the sadness of a friendship lost.