Shy and introversion are different things that result in similar social results when compared in a single scenario.
Being shy is a mild form of social anxiety. Which means the person is nervous, hesitant and uncomfortable with interacting with people even when they want to. Shy people are more likely to avoid conversation in the same way a fear of heights may prevent you from climbing the monkey bars despite seeing other kids having fun.
Introversion is a preference for solitary activity that is stronger than the preference for social interaction. So given the choice between going to a party and finally finishing that book, the introvert is more likely to prioritise the book.
Extroversion is a preference for group activity and social interaction. Given the choice between a party and reading, the party takes priority.
Between a shy person and an introvert both prefer to avoid socialising, so shy and introversion appear the same, especially when compared against the extrovert.
The more obvious difference between the shy person and the introvert is in their social skills. A shy person would have constant problems trying to handle new people and by choosing to avoid people they would rarely be able to practise their social skills. That becomes a perpetual cycle - no practice, no skills, no way to improve and get over the nervousness.
An introvert simply chooses not to socialise but doesn't have a problem interacting when required or when they want to. Therefore the introvert would be able to develop their social skills.
So the phrase "extremely outgoing and extremely introverted" isn't contradictory. It just means that when present in a single social situation the introvert in question is as outgoing as the extrovert. They just don't attend social situations as much compared to the extrovert.
For example, if you held a party twice a week for a month - At the same party you wouldn't be able to tell the difference between the introvert and the extrovert, but you would if you monitored their attendance over the month.
In (simplified) summary the shy person wants to socialise but can't, the introvert can but won't, the extrovert can and will while the outgoing person will socialise regardless of their ability.