To my thinking, the first conveys the idea of an event that still happening, she might have started the reading yesterday, be reading today and be reading tomorrow (or not, the "tomorrow" isn´t the most important part here). It can be something that is happening for a certain time, say, a course: she has been taking an English course/English lessons, etc.
To the second sentence (without elaborating more, as it is) - she is doing the reading right now. Regardless of which place she is (again, right now).
The "key" is that it happens at this precise moment/at the moment as we speak.