In many ways, terms such as "professional", "amateur", "semi-pro", "Beginner", "intermediate" and "advanced" are arbitrary. There is no world recognized body that mandates the level of a player. Players are judged only by reputation and consensus. Thit said, common sense would dictate that a player who plays in a very amateurish way and struggles to get through tunes is obviously an amateur beginner, and a player who plays magnificently and improvises with a confident voice is a more advanced player, possibly professional.
But what does it mean to be intermediate? My definition is as follows: A beginner player is almost solely dependent on the teacher to learn what and what not to play. He or she still needs to be taught stuff, and is lost without guidance. In contrast, an advanced player is a player who has the basics down, and is becoming increasingly self sufficient. He or she still learns from others (so too do all Jazz musicians as they try to constantly reinvent themselves), but at the same time, this person is capable of "getting out there" and learning and developing, even without hands on help.
In between is the intermediate player. By common sense, it is someone who is in between. The person still needs a strong teacher. He is or she is still struggling to master certain rudiments and may need very specific guidance and corrections -- on the other hand, a creative process is occurring in which the player is capable of engaging in self learning, although lack of efficiency and holes in basic knowledge may hinder progress leading to extended (and sometimes frustrating) learning plateaus that don't necessarily resolve themselves on their own.
This leads to the question of how intermediate players are taught. They key points are:
At this point, the player begins the transition to becoming a professional level player. My guess is that about 60-80% of players at amateur/"semi-pro" Jazz sessions and who come to me (and teachers such as myself) fall into this category. The good news is that most can make definitive leaps forward with the right teacher in surprisingly short periods of time. The bad news is that after years and years of having bad habits and attitudes instilled, many put up such a struggle that they become resistant to even the best teaching methods, and eventually give up and either stop making progress, or stop taking lessons. Therefore, the challenge of the teacher is to motivate and rehabilitate the student, in essence, helping the player to reinvent his or herself in order to make the ultimate game changing leap forward.