I always figured that was mostly just people-reading skills, recognizing body language and the like. But the original idea may have been that telepathy was long-range in its effects. I'm not sure how fully they thought it through.
The way I figured it was in Tin Man, not only could they sense people they're near or can see, but they can expand it beyond just one person but a general sense of those in a certain area near them.
The thing was that normal Betazoids could channel, focus and control what went into their heads..... buddy who went over to Tin Man couldn't and I believe he had another disability in that his telepathic abilities were far more advanced and could go quite a distance.
While most Betazoids could sense thoughts and emotions, Troi could only focus and interpret emotions, depending on who she focused on.