There is no line. Extraversion is a single continuous scale, scores on it are distributed like height with most people near the middle, and introvert and extrovert are the names for the two ends. Ambivert is simply the name for the crowded middle where most people are.
Why it feels like two types
The words come from Jung and were made into a two-way split by type-based tests, which sort everyone into one side or the other however close to the middle they fall. On a trait scale the same people are a smooth hump. The strip below shows the actual spread of extraversion scores in a sample of over 400,000 people: there is no gap, no second hump and no natural cut. Someone at the 48th percentile and someone at the 52nd are nearly identical, and a type test would call one an introvert and the other an extrovert.
What the scale actually measures
Extraversion is a bundle of related tendencies: warmth with people, liking for crowds, assertiveness, pace of life, appetite for excitement and cheerfulness. The 120-item test scores those six facets separately, and people often sit high on some and low on others: a quiet person who takes charge, or a sociable person who hates risk. Judge and colleagues (2002) found extraversion the Big Five trait most strongly linked to leadership, and Ozer and Benet-MartÃnez (2006) list its links to happiness and social relationships, but those are averages across whole populations, not predictions about anyone.
What introversion is not
It is not shyness. Shyness is discomfort or fear around people; introversion is a preference for less stimulation and smaller company, and the two are only loosely related. It is not a lack of social skill, and it is not a deficit: a low score describes a person who recovers alone, thinks before speaking and likes a few people deeply.
What it means for your results
Read your percentile, not a label. If you are between the 25th and the 75th percentile you are like most people on this trait, however the words make you feel. If you are near an end, the facets will tell you which parts of extraversion drive it. And if a type test once told you which side of the line you were on, the strip shows how little a line means.