My take on it is that Avantgarde is about coming up with new forms, so as such usually has choicely placed read arranged parts to distinguish between the turkey and meatloaf. Whereas free jazz is just a reversion to more comfortable forms.
I think you need to do a little digging into jazz first, it sounds like you might be a little confused. Free jazz is jazz that is free from traditional contstraints, like harmony, rhythm, and form. Check out the youtube link in my last post, that is quintessential Free jazz.
Avant garde is cutting edge music, so it;s difficult to define, but if you look at John Zorn, there is form, but not in the traditional sense. Here are some clips from his Naked City album (one of his most popular). I know htis is from the late 80s, but this is still considered avant garde, even if it's a little dated.
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=video&cd=4&cad=rja&uact=8&ved=0ahUKEwiAv7r40LjKAhUhk4MKHamRACcQtwIIJTAD&url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D-HLY6ucn674&usg=AFQjCNG-Y6xqxCtJOlz9rWrsTWFHc4Kfqw&sig2=mOKokt_PP9Vb5YQpKtPZ8A&bvm=bv.112064104,d.amc
BeBop or Bop based on a big name soloist over a rhythm section playing a form was eclipsed by Hard Bop which consisted of a smaller ensemble playing tighter choreographed arrangements. Cool Jazz, Bossa Nova, Funk etc. all have specific forms, but the drums have specific parts in each song.
Again, I think you need to dig a little deeper into jazz and its history. Big Name soloists over a rhythm section was called swing, these are players like Coleman Hawkins who were replaced by bebop. This was popular from the 30s until around the mid 1940s.
Bebop were smaller groups playing less arranged standards at a much faster pace. Bebop was early 40s - early 50s.
Hard bop was the inclusion of gospel and R&B influences into bop playing. Typically hard bop was played at (slightly) slower tempos
Cool jazz also came about in the 1950s as a reaction to the fast pace of hard bop and post bop. Cool jazz used relaxed tempos and softer tones than bebop (think Miles Davis And Chet Baker).
Bossa Nova became popular with jazz musicians in the 1960s, but isn't really a jazz genre. Often jazz players will play a bossa nova form and rhythm and improvise over it (Stan Getz).
Funk is not jazz and comes from R&B influences. In the 70s jazz started to fuse with funk, but on its own funk is not jazz.
Anyway, the opinion that you can just jam-O-long to any Jazz song using the form is too popular to rebut on this forum whether it is true or not, and I don't care about it that much. Let's just say that there are differing opinions on to what extent jazz is actually improvised, and that a large portion of jazz is not. Eg Big Band.
No one's "jamming along", I think you aren't getting some of the core concepts of jazz. Jazz is about interpretation and interaction. This goes all the way to the roots of jazz in Congo Square.
I'd say that there aren't any differing opinions on the subject; improvisation is at the core of jazz. Big Band was heavily arranged, as it was dance music, but there was still improvisation. Based on some of your responses, it sounds like you aren't that familiar with jazz. Look up Ted Gioia's The History of Jazz. That's a great resource that might help you with the timeline of jazz and the trends. It will take you from the 1890s up to today, and might help you get a better understanding.