I think "boundary experience" refers to a challenging moment when you're having to deal with (you're confronted with) something foreign and very different .... for instance, you could be dealing with people from a different cultural background, with different perspectives etc .... and "threshold experience" is the process of adapting and aligning your way of thinking to accommodate this challenging new environment and an opportunity to grow as a person?
So, "boundary experience" is like culture shock, in a way (maybe culture shock is one example of it??), and "threshold experience" is the opportunity for a positive, personal growth experience, by adapting to this challenge (with the realigning of thoughts/perspectives) and the releasing of this tension?
Although they are closely related concepts, they are different ... and I couldn't divine that from Alexandra's 3 line quote. It sounded like "boundary" and "threshold" were more or less one and the same (based on what I knew about threshold experiences).
"Boundaries" are frames of references - what you believe in, how you think, etc... and might become rigid structures over time.
Quite a bit of guesswork ... but I came across an article on student/teacher relationships, which helped (I couldn't refer to any of the philosophy texts)
Please delete all (or whichever of my above posts, feel free).
Apologies - it was a learning experience for me - and a waste of time for everyone else. I hope not.